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Recent Ebola virus disease infections have been limited to human-to-human contact as well as the intricate linkages between the habitat, people and socioeconomic variables. The mechanisms of infection propagation can also occur as a consequence of variations in individual actions brought on by dread. This work studies the evolution of the Ebola virus disease by combining fear and environmental spread using a compartmental framework considering stochastic manipulation and a newly defined non-local fractal-fractional (F-F) derivative depending on the generalized Mittag-Leffler kernel. To determine the incidence of infection and person-to-person dissemination, we developed a fear-dependent interaction rate function. We begin by outlining several fundamental characteristics of the system, such as its fundamental reproducing value and equilibrium. Moreover, we examine the existence-uniqueness of non-negative solutions for the given randomized process. The ergodicity and stationary distribution of the infection are then demonstrated, along with the basic criteria for its eradication. Additionally, it has been studied how the suggested framework behaves under the F-F complexities of the Atangana-Baleanu derivative of fractional-order $ \rho $ and fractal-dimension $ \tau $. The developed scheme has also undergone phenomenological research in addition to the combination of nonlinear characterization by using the fixed point concept. The projected findings are demonstrated through numerical simulations. This research is anticipated to substantially increase the scientific underpinnings for understanding the patterns of infectious illnesses across the globe.

These fundamental Theorems of classical analysis, namely Baire's Theorem and Cantor's Intersection Theorem in the context of Neutrosophic 2-metric spaces, are demonstrated in this article. Naschie discussed high energy physics in relation to the Baire's Theorem and the Cantor space in descriptive set theory. We describe, how to demonstrate the validity and uniqueness of the common fixed-point theorem for four mappings in Neutrosophic 2-metric spaces.

By combining the results of Wardowski's cyclic contraction operators and admissible multi-valued mappings, the motif of $ \eta $-cyclic $ \left(\alpha _{\ast }, \beta _{\ast }\right) $-admissible type $ \digamma $-contraction multivalued mappings are presented. Moreover, some novel fixed point theorems for such mappings are proved in the context of $ M_{b} $-metric spaces. Also, two examples are given to clarify and strengthen our theoretical study. Finally, the existence of a solution of a pair of ordinary differential equations is discussed as an application.

In this manuscript, the concept of rational-type multivalued $ F- $contraction mappings is investigated. In addition, some nice fixed point results are obtained using this concept in the setting of $ MM- $spaces and ordered $ MM- $spaces. Our findings extend, unify, and generalize a large body of work along the same lines. Moreover, to support and strengthen our results, non-trivial and extensive examples are presented. Ultimately, the theoretical results are involved in obtaining a positive, definite solution to nonlinear matrix equations as an application.

In this paper, we introduce the notion of an orthogonal neutrosophic rectangular metric space and prove fixed point theorems. We extend some of the well-known results in the literature. As applications of the main results, we apply our main results to show the existence of a unique solution.

In this research, we investigate the dynamical behaviour of a HPAI epidemic system featuring a half-saturated transmission rate and significant evidence of crossover behaviours. Although simulations have proposed numerous mathematical frameworks to portray these behaviours, it is evident that their mathematical representations cannot adequately describe the crossover behaviours, particularly the change from deterministic reboots to stochastics. Furthermore, we show that the stochastic process has a threshold number $ {\bf R}_{0}^{s} $ that can predict pathogen extermination and mean persistence. Furthermore, we show that if $ {\bf R}_{0}^{s} > 1 $, an ergodic stationary distribution corresponds to the stochastic version of the aforementioned system by constructing a sequence of appropriate Lyapunov candidates. The fractional framework is expanded to the piecewise approach, and a simulation tool for interactive representation is provided. We present several illustrated findings for the system that demonstrate the utility of the piecewise estimation technique. The acquired findings offer no uncertainty that this notion is a revolutionary viewpoint that will assist mankind in identifying nature.

In this work, the existence of solutions for nonlinear hybrid fractional integro-differential equations involving generalized proportional fractional (GPF) derivative of Caputo-Liouville-type and multi-term of GPF integrals of Reimann-Liouville type with Dirichlet boundary conditions is investigated. The analysis is accomplished with the aid of the Dhage's fixed point theorem with three operators and the lower regularized incomplete gamma function. Further, the uniqueness of solutions and their Ulam-Hyers-Rassias stability to a special case of the suggested hybrid problem are discussed. For the sake of corroborating the obtained results, an illustrative example is presented.

In this research, we investigate the direct interaction acquisition method to create a stochastic computational formula of cholera infection evolution via the fractional calculus theory. Susceptible people, infected individuals, medicated individuals, and restored individuals are all included in the framework. Besides that, we transformed the mathematical approach into a stochastic model since it neglected the randomization mechanism and external influences. The descriptive behaviours of systems are then investigated, including the global positivity of the solution, ergodicity and stationary distribution are carried out. Furthermore, the stochastic reproductive number for the system is determined while for the case $ \mathbb{R}_{0}^{s} > 1, $ some sufficient condition for the existence of stationary distribution is obtained. To test the complexity of the proposed scheme, various fractional derivative operators such as power law, exponential decay law and the generalized Mittag-Leffler kernel were used. We included a stochastic factor in every case and employed linear growth and Lipschitz criteria to illustrate the existence and uniqueness of solutions. So every case was numerically investigated, utilizing the newest numerical technique. According to simulation data, the main significant aspects of eradicating cholera infection from society are reduced interaction incidence, improved therapeutic rate, and hygiene facilities.

Decision-making in a vague, undetermined and imprecise environment has been a great issue in real-life problems. Many mathematical theories like fuzzy, intuitionistic and neutrosophic sets have been proposed to handle such kinds of environments. Intuitionistic fuzzy sets (IFSS) were formulated by Atanassov in 1986 and analyze the truth membership, which assists in evidence, along with the fictitious membership. This article describes a composition of the intuitionistic fuzzy set (IFS) with the hypersoft set, which assists in coping with multi-attributive decision-making issues. Similarity measures are the tools to determine the similarity index, which evaluates how similar two objects are. In this study, we develop some distance and similarity measures for IFHSS with the help of aggregate operators. Also, we prove some new results, theorems and axioms to check the validity of the proposed study and discuss a real-life problem. The air quality index (AQI) is one of the major factors of the environment which is affected by air pollution. Air pollution is one of the extensive worldwide problems, and now it is well acknowledged to be deleterious to human health. A decision-maker determines ϸ = region (different geographical areas) and the factors$ \{\mathrm{ᵹ}=human~~activiteis,\mathrm{Ϥ}=humidity~~level,\zeta =air~~pollution\} $ which enhance the AQI by applying decision-making techniques. This analysis can be used to determine whether a geographical area has a good, moderate or hazardous AQI. The suggested technique may also be applied to a large number of the existing hypersoft sets. For a remarkable environment, alleviating techniques must be undertaken.

With the fast growth of the economy and rapid urbanization, the waste produced by the urban population also rises as the population increases. Due to communal, ecological, and financial constrictions, indicating a landfill site has become perplexing. Also, the choice of the landfill site is oppressed with vagueness and complexity due to the deficiency of information from experts and the existence of indeterminate data in the decision-making (DM) process. The neutrosophic hypersoft set (NHSS) is the most generalized form of the neutrosophic soft set, which deals with the multi-sub-attributes of the alternatives. The NHSS accurately judges the insufficiencies, concerns, and hesitation in the DM process compared to IFHSS and PFHSS, considering the truthiness, falsity, and indeterminacy of each sub-attribute of given parameters. This research extant the operational laws for neutrosophic hypersoft numbers (NHSNs). Furthermore, we introduce the aggregation operators (AOs) for NHSS, such as neutrosophic hypersoft weighted average (NHSWA) and neutrosophic hypersoft weighted geometric (NHSWG) operators, with their necessary properties. Also, a novel multi-criteria decision-making (MCDM) approach has been developed for site selection of solid waste management (SWM). Moreover, a numerical description is presented to confirm the reliability and usability of the proposed technique. The output of the advocated algorithm is compared with the related models already established to regulate the favorable features of the planned study.

Dengue viruses have distinct viral regularities due to the their serotypes. Dengue can be aggravated from a simple fever in an acute infection to a presumably fatal secondary pathogen. This article investigates a deterministic-stochastic secondary dengue viral infection (SDVI) model including logistic growth and a nonlinear incidence rate through the use of piecewise fractional differential equations. This framework accounts for the fact that the dengue virus can penetrate various kinds of specific receptors. Because of the supplementary infection, the system comprises both heterologous and homologous antibody. For the deterministic case, we determine the invariant region and threshold for the aforesaid model. Besides that, we demonstrate that the suggested stochastic SDVI model yields a global and non-negative solution. Taking into consideration effective Lyapunov candidates, the sufficient requirements for the presence of an ergodic stationary distribution of the solution to the stochastic SDVI model are generated. This report basically utilizes a novel idea of piecewise differentiation and integration. This method aids in the acquisition of mechanisms, including crossover impacts. Graphical illustrations of piecewise modeling techniques for chaos challenges are demonstrated. A piecewise numerical scheme is addressed. For various cases, numerical simulations are presented.

This article adopts a class of nonlinear fractional differential equation associating Hilfer generalized proportional fractional ($ GPF $) derivative with having boundary conditions, which amalgamates the Riemann-Liouville $ (RL) $ and Caputo-$ GPF $ derivative. Taking into consideration the weighted space continuous mappings, we first derive a corresponding integral for the specified boundary value problem. Also, we investigate the existence consequences for a certain problem with a new unified formulation considering the minimal suppositions on nonlinear mapping. Detailed developments hold in the analysis and are dependent on diverse tools involving Schauder's, Schaefer's and Kransnoselskii's fixed point theorems. Finally, we deliver two examples to check the efficiency of the proposed scheme.

In this work, we prove existence and uniqueness fixed point theorems under Banach and Kannan type contractions on $ \mathcal{C}^{\star} $-algebra-valued bipolar metric spaces. To strengthen our main results, an appropriate example and an effective application are presented.

In this paper, we introduce orthogonal generalized $ {\bf{O}} $-$ {\boldsymbol{\alpha}} $-$ {\boldsymbol{\psi}} $-Geraghty contractive type mappings and prove some fixed point theorems in $ {\bf{O}} $-complete $ {\bf{O}} $-$ \mathfrak{b} $-metric spaces. We also provide an illustrative example to support our theorem. The results proved here will be utilized to show the existence of a solution to an integral equation as an application.

In this work, we apply the reproducing kernel method to coupled system of second and fourth order boundary value problems. We construct a novel algorithm to acquire the numerical results of the nonlinear boundary-value problems. We also use the Legendre polynomials. Additionally, we discuss the convergence analysis and error estimates. We demonstrate the numerical simulations to prove the efficiency of the presented method.

Monkeypox ($ \mathbb{MPX} $) is a zoonotic illness that is analogous to smallpox. Monkeypox infections have moved across the forests of Central Africa, where they were first discovered, to other parts of the world. It is transmitted by the monkeypox virus, which is a member of the Poxviridae species and belongs to the Orthopoxvirus genus. In this article, the monkeypox virus is investigated using a deterministic mathematical framework within the Atangana-Baleanu fractional derivative that depends on the generalized Mittag-Leffler (GML) kernel. The system's equilibrium conditions are investigated and examined for robustness. The global stability of the endemic equilibrium is addressed using Jacobian matrix techniques and the Routh-Hurwitz threshold. Furthermore, we also identify a criterion wherein the system's disease-free equilibrium is globally asymptotically stable. Also, we employ a new approach by combining the two-step Lagrange polynomial and the fundamental concept of fractional calculus. The numerical simulations for multiple fractional orders reveal that as the fractional order reduces from 1, the virus's transmission declines. The analysis results show that the proposed strategy is successful at reducing the number of occurrences in multiple groups. It is evident that the findings suggest that isolating affected people from the general community can assist in limiting the transmission of pathogens.

Mathematical applications in engineering have a long history. One of the most well-known analytical techniques, the optimal variational iteration method (OVIM), is utilized to construct a quick and accurate algorithm for a special fourth-order ordinary initial value problem. Many researchers have discussed the problem involving a parameter c. We solve the parametric boundary value problem that can't be addressed using conventional analytical methods for greater values of c using a new method and a convergence control parameter h. We achieve a convergent solution no matter how huge c is. For the approximation of the convergence control parameter h, two strategies have been discussed. The advantages of one technique over another have been demonstrated. Optimal variational iteration method can be seen as an effective technique to solve parametric boundary value problem.

In this paper, using positive symmetric functions, we offer two new important identities of fractional integral form for convex and harmonically convex functions. We then prove new variants of the Hermite-Hadamard-Fejér type inequalities for convex as well as harmonically convex functions via fractional integrals involving an exponential kernel. Moreover, we also present improved versions of midpoint type Hermite-Hadamard inequality. Graphical representations are given to validate the accuracy of the main results. Finally, applications associated with matrices, q-digamma functions and modifed Bessel functions are also discussed.

Over time, the interpolative approach in fixed point theory (FPT) has been investigated only in the setting of crisp mathematics, thereby dropping-off a significant amount of useful results. As an attempt to fill up the aforementioned gaps, this paper initiates certain hybrid concepts under the names of interpolative Hardy-Rogers-type (IHRT) and interpolative Reich-Rus-Ciric type (IRRCT) intuitionistic fuzzy contractions in the frame of metric space (MS). Adequate criteria for the existence of intuitionistic fuzzy fixed point (FP) for such contractions are examined. On the basis that FP of a single-valued mapping obeying interpolative type contractive inequality is not always unique, and thereby making the ideas more suitable for FP theorems of multi-valued mappings, a few special cases regarding point-to-point and non-fuzzy set-valued mappings which include the conclusions of some well-known results in the corresponding literature are highlighted and discussed. In addition, comparative examples which dwell on the generality of our obtained results are constructed.

In this paper, we establish the concept of controlled neutrosophic metric-like spaces as a generalization of neutrosophic metric spaces and provide several non-trivial examples to show the spuriousness of the new concept in the existing literature. Furthermore, we prove several fixed point results for contraction mappings and provide the examples with their graphs to show the validity of the results. At the end of the manuscript, we establish an application to integral equations, in which we use the main result to find the solution of the integral equation.

Recently, researchers have become interested in modelling, monitoring, and treatment of hepatitis B virus infection. Understanding the various connections between pathogens, immune systems, and general liver function is crucial. In this study, we propose a higher-order stochastically modified delay differential model for the evolution of hepatitis B virus transmission involving defensive cells. Taking into account environmental stimuli and ambiguities, we presented numerical solutions of the fractal-fractional hepatitis B virus model based on the exponential decay kernel that reviewed the hepatitis B virus immune system involving cytotoxic T lymphocyte immunological mechanisms. Furthermore, qualitative aspects of the system are analyzed such as the existence-uniqueness of the non-negative solution, where the infection endures stochastically as a result of the solution evolving within the predetermined system's equilibrium state. In certain settings, infection-free can be determined, where the illness settles down tremendously with unit probability. To predict the viability of the fractal-fractional derivative outcomes, a novel numerical approach is used, resulting in several remarkable modelling results, including a change in fractional-order $ \delta $ with constant fractal-dimension $ \varpi $, $ \delta $ with changing $ \varpi $, and $ \delta $ with changing both $ \delta $ and $ \varpi $. White noise concentration has a significant impact on how bacterial infections are treated.

Our aim is to introduce the notion of $ N_{b} $-fuzzy metric space (FMS). We also define quasi $ N $-FMS, and pseudo $ N_{b} $-FMS with examples and counterexamples and prove a decomposition theorem for pseudo $ N_{b} $-FMS. We prove various theorems related to the convergence of sequences and analyze topology of symmetric $ N_{b} $-FMS. At last, we provide an application of $ q $-contraction mapping as a Banach contraction principle (BCP) in the structure of symmetric $ N_{b} $-FMS and applied it in the solution of integral equations and linear equations.

In this research, the $ \bar{\mathbf{q}} $-homotopy analysis transform method ($ \bar{\mathbf{q}} $-HATM) is employed to identify fractional-order Whitham–Broer–Kaup equation (WBKE) solutions. The WBKE is extensively employed to examine tsunami waves. With the aid of Caputo and Atangana-Baleanu fractional derivative operators, to obtain the analytical findings of WBKE, the predicted algorithm employs a combination of $ \bar{\mathbf{q}} $-HAM and the Aboodh transform. The fractional operators are applied in this work to show how important they are in generalizing the frameworks connected with kernels of singularity and non-singularity. To demonstrate the applicability of the suggested methodology, various relevant problems are solved. Graphical and tabular results are used to display and assess the findings of the suggested approach. In addition, the findings of our recommended approach were analyzed in relation to existing methods. The projected approach has fewer processing requirements and a better accuracy rate. Ultimately, the obtained results reveal that the improved strategy is both trustworthy and meticulous when it comes to assessing the influence of nonlinear systems of both integer and fractional order.

The point of this work was to analyze and investigate the sufficient conditions of the existence and uniqueness of solutions for the nonlinear fuzzy fractional Volterra Fredholm integro-differential equation in the frame of the Atangana-Baleanu-Caputo fractional derivative methodology. To begin with, we give the parametric interval form of the Atangana-Baleanu-Caputo fractional derivative on fuzzy set-valued functions. Then, by employing Schauder's and Banach's fixed point procedures, we examine the existence and uniqueness of solutions for fuzzy fractional Volterra Fredholm integro-differential equation with the Atangana-Baleanu-Caputo fractional operator. It turns out that the last interval model is a combined arrangement of nonlinear equations. In addition, we consider results by applying the Adams Bashforth fractional technique and present two examples that have been numerically solved using graphs.

In this study, the transmission dynamics of Contagious Bovine Pleuropneumonia (CBPP) by finite difference method are presented. This model is made up of sensitive, exposed, vaccinated, infectious, constantly infected, and treated compartments. The model is studied by the finite difference method. Firstly, the finite difference scheme is constructed. Then the stability estimates are proved for this model. As a result, several simulations are given for this model on the verge of antibiotic therapy. From these figures, the supposition that 50% of infectious cattle take antibiotic therapy or the date of infection decrease to 28 days, 50% of susceptible obtain vaccination within 73 days.

Divorce is the dissolution of two parties' marriage. Separation and divorce are the major obstacles to the viability of a stable family dynamic. In this research, we employ a basic incidence functional as the source of interpersonal disagreement to build an epidemiological framework of divorce outbreaks via the fractal-fractional technique in the Atangana-Baleanu perspective. The research utilized Lyapunov processes to determine whether the two steady states (divorce-free and endemic steady state point) are globally asymptotically robust. Local stability and eigenvalues methodologies were used to examine local stability. The next-generation matrix approach also provides the fundamental reproducing quantity $ \bar{\mathbb{R}_{0}} $. The existence and stability of the equilibrium point can be assessed using $ \bar{\mathbb{R}}_0 $, demonstrating that counseling services for the separated are beneficial to the individuals' well-being and, as a result, the population. The fractal-fractional Atangana-Baleanu operator is applied to the divorce epidemic model, and an innovative technique is used to illustrate its mathematical interpretation. We compare the fractal-fractional model to a framework accommodating different fractal-dimensions and fractional-orders and deduce that the fractal-fractional data fits the stabilized marriages significantly and cannot break again.

The SARS-CoV-2 virus pandemic remains a pressing issue with its unpredictable nature, and it spreads worldwide through human interaction. Current research focuses on the investigation and analysis of fractional epidemic models that discuss the temporal dynamics of the SARS-CoV-2 virus in the community. In this work, we choose a fractional-order mathematical model to examine the transmissibility in the community of several symptoms of COVID-19 in the sense of the Caputo operator. Sensitivity analysis of $ R_{0} $ and disease-free local stability of the system are checked. Also, with the assistance of fixed point theory, we demonstrate the existence and uniqueness of the system. In addition, numerically we solve the fractional model and presented some simulation results via actual estimation parameters. Graphically we displayed the effects of numerous model parameters and memory indexes. The numerical outcomes show the reliability, validation, and accuracy of the scheme.

Recently different definitions of fractional derivatives are proposed for the development of real-world systems and mathematical models. In this paper, our main concern is to develop and analyze the effective numerical method for fractional order HIV/ AIDS model which is advanced approach for such biological models. With the help of an effective techniques and Sumudu transform, some new results are developed. Fractional order HIV/AIDS model is analyzed. Analysis for proposed model is new which will be helpful to understand the outbreak of HIV/AIDS in a community and will be helpful for future analysis to overcome the effect of HIV/AIDS. Novel numerical procedures are used for graphical results and their discussion.

The main objective of the investigation is to broaden the description of Caputo fractional derivatives (in short, CFDs) (of order $ 0 < \alpha < r $) considering all relevant permutations of entities involving $ t_{1} $ equal to $ 1 $ and $ t_{2} $ (the others) equal to $ 2 $ via fuzzifications. Under $ {g\mathcal{H}} $-differentiability, we also construct fuzzy Elzaki transforms for CFDs for the generic fractional order $ \alpha\in(r-1, r) $. Furthermore, a novel decomposition method for obtaining the solutions to nonlinear fuzzy fractional partial differential equations (PDEs) via the fuzzy Elzaki transform is constructed. The aforesaid scheme is a novel correlation of the fuzzy Elzaki transform and the Adomian decomposition method. In terms of CFD, several new results for the general fractional order are obtained via $ g\mathcal{H} $-differentiability. By considering the triangular fuzzy numbers of a nonlinear fuzzy fractional PDE, the correctness and capabilities of the proposed algorithm are demonstrated. In the domain of fractional sense, the schematic representation and tabulated outcomes indicate that the algorithm technique is precise and straightforward. Subsequently, future directions and concluding remarks are acted upon with the most focused use of references.

The main idea of this study is to examine the dynamics of the viral disease, hepatitis C. To this end, the steady states of the hepatitis C virus model are described to investigate the local as well as global stability. It is proved by the standard results that the virus-free equilibrium state is locally asymptotically stable if the value of $ R_0 $ is taken less than unity. Similarly, the virus existing state is locally asymptotically stable if $ R_0 $ is chosen greater than unity. The Routh-Hurwitz criterion is applied to prove the local stability of the system. Further, the disease-free equilibrium state is globally asymptotically stable if $ R_0 < 1 $. The viral disease model is studied after reshaping the integer-order hepatitis C model into the fractal-fractional epidemic illustration. The proposed numerical method attains the fixed points of the model. This fact is described by the simulated graphs. In the end, the conclusion of the manuscript is furnished.

The majority of infectious illnesses, such as HIV/AIDS, Hepatitis, and coronavirus (2019-nCov), are extremely dangerous. Due to the trial version of the vaccine and different forms of 2019-nCov like beta, gamma, delta throughout the world, still, there is no control on the transmission of coronavirus. Delay factors such as social distance, quarantine, immigration limitations, holiday extensions, hospitalizations, and isolation are being utilized as essential strategies to manage the outbreak of 2019-nCov. The effect of time delay on coronavirus disease transmission is explored using a non-linear fractional order in the Caputo sense in this paper. The existence theory of the model is investigated to ensure that it has at least one and unique solution. The Ulam-Hyres (UH) stability of the considered model is demonstrated to illustrate that the stated model's solution is stable. To determine the approximate solution of the suggested model, an efficient and reliable numerical approach (Adams-Bashforth) is utilized. Simulations are used to visualize the numerical data in order to understand the behavior of the different classes of the investigated model. The effects of time delay on dynamics of coronavirus transmission are shown through numerical simulations via MATLAB-17.

The momentous objective of this work is to discuss some qualitative properties of solutions such as the estimate of the solutions, the continuous dependence of the solutions on initial conditions and the existence and uniqueness of extremal solutions to a new class of fractional differential equations involving two fractional derivatives in the sense of Caputo fractional derivative with respect to another function $ \Phi $. Firstly, using the generalized Laplace transform method, we give an explicit formula of the solutions to the aforementioned linear problem which can be regarded as a novelty item. Secondly, by the implementation of the $ \Phi $-fractional Gronwall inequality, we analyze some properties such as estimates and continuous dependence of the solutions on initial conditions. Thirdly, with the help of features of the Mittag-Leffler functions (MLFs), we build a new comparison principle for the corresponding linear equation. This outcome plays a vital role in the forthcoming analysis of this paper especially when we combine it with the monotone iterative technique alongside facet with the method of upper and lower solutions to get the extremal solutions for the analyzed problem. Lastly, we present some examples to support the validity of our main results.

Swift-Hohenberg equations are frequently used to model the biological, physical and chemical processes that lead to pattern generation, and they can realistically represent the findings. This study evaluates the Elzaki Adomian decomposition method (EADM), which integrates a semi-analytical approach using a novel hybridized fuzzy integral transform and the Adomian decomposition method. Moreover, we employ this strategy to address the fractional-order Swift-Hohenberg model (SHM) assuming g$ {\bf H} $-differentiability by utilizing different initial requirements. The Elzaki transform is used to illustrate certain characteristics of the fuzzy Atangana-Baleanu operator in the Caputo framework. Furthermore, we determined the generic framework and analytical solutions by successfully testing cases in the series form of the systems under consideration. Using the synthesized strategy, we construct the approximate outcomes of the SHM with visualizations of the initial value issues by incorporating the fuzzy factor $ \varpi\in[0, 1] $ which encompasses the varying fractional values. Finally, the EADM is predicted to be effective and precise in generating the analytical results for dynamical fuzzy fractional partial differential equations that emerge in scientific disciplines.

Defining new fractional operators and employing them to establish well-known integral inequalities has been the recent trend in the theory of mathematical inequalities. To take a step forward, we present novel versions of Hermite-Hadamard type inequalities for a new fractional operator, which generalizes some well-known fractional integral operators. Moreover, a midpoint type fractional integral identity is derived for differentiable mappings, whose absolute value of the first-order derivatives are convex functions. Moreover, considering this identity as an auxiliary result, several improved inequalities are derived using some fundamental inequalities such as Hölder-İşcan, Jensen and Young inequality. Also, if we take the parameter $ \rho = 1 $ in most of the results, we derive new results for Atangana-Baleanu equivalence. One example related to matrices is also given as an application.

In this paper, we obtain some coupled fixed point theorems on a bicomplex partial metric space. An example and an application to support our result are presented.

In this article, an analytical and numerical analysis of a computer virus epidemic model is presented. To more thoroughly examine the dynamics of the virus, the classical model is transformed into a fractional order model. The Caputo differential operator is applied to achieve this. The Jacobian approach is employed to investigate the model's stability. To investigate the model's numerical solution, a hybridized numerical scheme called the Grunwald Letnikov nonstandard finite difference (GL-NSFD) scheme is created. Some essential characteristics of the population model are scrutinized, including positivity boundedness and scheme stability. The aforementioned features are validated using test cases and computer simulations. The mathematical graphs are all detailed. It is also investigated how the fundamental reproduction number $ \mathfrak{R}_0 $ functions in stability analysis and illness dynamics.

In this work, we introduce and study a class of Langevin equation with nonlocal boundary conditions governed by a Caputo fractional order proportional derivatives of an unknown function with respect to another function. The qualitative results concerning the given problem are obtained with the aid of the lower regularized incomplete Gamma function and applying the standard fixed point theorems. In order to homologate the theoretical results we obtained, we present two examples.

HIV-1 infection is a dangerous diseases like Cancer, AIDS, etc. Many mathematical models have been introduced in the literature, which are investigated with different approaches. In this article, we generalize the HIV-1 model through nonsingular fractional operator. The non-integer mathematical model of HIV-1 infection under the Caputo-Fabrizio derivative is presented in this paper. The concept of Picard-Lindelof and fixed-point theory are used to address the existence of a unique solution to the HIV-1 model under the suggested operator. Also, the stability of the suggested model is proved through the Picard iteration and fixed point theory approach. The model's approximate solution is constructed through three steps Adams-Bashforth numerical method. Numerical simulations are provided for different values of fractional-order to study the complex dynamics of the model. Lastly, we provide the oscillatory and chaotic behavior of the proposed model for various fractional orders.

In this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary differential equations in the frame of the fractional derivatives under discussion.

In this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary differential equations in the frame of the fractional derivatives under discussion.

In this paper, some new inequalities of Simpson's type are set up for the classes of functions whose derivatives of absolute are preinvex by means of $% \kappa$-fractional integrals. Additionally, by extraordinary choices of $n$ and $\kappa$, we give some diminished outcomes. Meanwhile, we also provide the inequalities for $\mathcal{F}$-divergence measures and in probabilistic versions.

In this paper, we establish the Lyapunov-type inequality for boundary value problems involving generalized Caputo fractional derivatives that unite the Caputo and Caputo-Hadamrad fractional derivatives. An application about the zeros of generalized types of Mittag-Leffler functions is given.

This paper aims to investigate the several generalizations by newly proposed generalized \begin{document}$ \mathcal{K} $\end{document} -fractional conformable integral operator. Based on these novel ideas, we derived a novel framework to study for \begin{document}$ \breve{C} $\end{document} eby \begin{document}$ \breve{s} $\end{document} ev and P \begin{document}$ \acute{o} $\end{document} lya-Szeg \begin{document}$ \ddot{o} $\end{document} type inequalities by generalized \begin{document}$ \mathcal{K} $\end{document} -fractional conformable integral operator. Several special cases are apprehended in the light of generalized fractional conformable integral. This novel strategy captures several existing results in the relative literature. We also aim at showing important connections of the results here with those including Riemann-Liouville fractional integral operator.

In this paper, we present a new approach to solving the problem of interpolating a continuous function at \begin{document}$ (n+1) $\end{document} equally-spaced points in the interval \begin{document}$ [0, 1] $\end{document} , using shifts of a kernel on the \begin{document}$ (1/n) $\end{document} -spaced infinite grid. The archetypal example here is approximation using shifts of a Gaussian kernel. We present new results concerning interpolation of functions of exponential type, in particular, polynomials on the integer grid as a step en route to solve the general interpolation problem. For the Gaussian kernel we introduce a new class of polynomials, closely related to the probabilistic Hermite polynomials and show that evaluations of the polynomials at the integer points provide the coefficients of the interpolants. Finally we give a closed formula for the Gaussian interpolant of a continuous function on a uniform grid in the unit interval (assuming knowledge of the discrete moments of the Gaussian).

In this paper, we study initial/boundary value problems for \begin{document}$ 1+1 $\end{document} dimensional and \begin{document}$ 1+2 $\end{document} dimensional fractional order telegraph equations. We develop the technique of double and triple Laplace transforms and obtain exact analytical solutions of these problems. The techniques we develop are new and are not limited to only telegraph equations but can be used for exact solutions of large class of linear fractional order partial differential equations

The present article deals with the new estimates in the view of generalized proportional fractional integral with respect to another function. In the present investigation, we focus on driving certain new classes of integral inequalities utilizing a family of positive functions \begin{document}$ n(n\in\mathbb{N}) $\end{document} for this newly defined operator. From the computed outcomes, we concluded some new variants for classical generalized proportional fractional and other integrals as remarks. These variants are connected with some existing results in the literature. Certain interesting consequent results of the main theorems are also pointed out.

This paper studies a class of fourth point singular boundary value problem of \begin{document}$ p $\end{document}-Laplacian operator in the setting of a specific kind of conformable derivatives. By using the upper and lower solutions method and fixed point theorems on cones., necessary and sufficient conditions for the existence of positive solutions are obtained. In addition, we investigate the dependence of the solution on the order of the conformable differential equation and on the initial conditions.