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In this article, we establish a new class of mixed integral fractional delay dynamic systems with impulsive effects on time scales. We investigate the qualitative properties of the considered systems. In fact, the article contains three segments, and the first segment is devoted to investigating the existence and uniqueness results. In the second segment, we study the stability analysis, while the third segment is devoted to investigating the controllability criterion. We use the Leray–Schauder and Banach fixed point theorems to prove our results. Moreover, the obtained results are examined with the help of an example. [ABSTRACT FROM AUTHOR]

Rapid emissions of green-house gases (GHGs) are causing global warming, which is wreaking havoc on the earth's climate system. As a result, the coastal ecosystems of the world are on the verge of becoming endangered. We develop a fractal-fractional hybrid model to estimate the influence of rapid emissions of GHGs on the coastal ecosystems and climate changes. The fractal-fractional climate change model is considered for the theoretical and numerical aspects. The theoretical aspect includes the existence and Hyers–Ulam (HU) stability of the solutions while the numerical aspect is based on Lagrange's interpolation polynomial. Moreover, unique solutions are proved by the Banach contraction principle. Different fractal-fractional orders are considered for the numerical study of dynamics of solutions which prove the importance and accuracy of these hybrid operators. [ABSTRACT FROM AUTHOR]

In this work, we consider a generalized quantum fractional Sturm–Liouville–Langevin difference problem with terminal boundary conditions. The relevant results rely on Mönch's fixed point theorem along with a theoretical method by terms of Kuratowski measure of noncompactness (MNC) and the Banach contraction principle (BCP). Furthermore, two dynamical notions of Ulam–Hyers (UH) and generalized Ulam–Hyers (GUH) stability are addressed for solutions of the supposed Sturm–Liouville–Langevin quantum boundary value problem (q-FBVP). Two examples are presented to show the validity and also the effectiveness of theoretical results. In the last part of the paper, we conclude our exposition with some final remarks and observations. [ABSTRACT FROM AUTHOR]

In this paper, the existence, uniqueness and stability of solutions to a boundary value problem of nonlinear FDEs of variable order are established. To do this, we first investigate some aspects of variable order operators of Hadamard type. Then, with the help of the generalized intervals and piecewise constant functions, we convert the variable order Hadamard FBVP to an equivalent standard Hadamard BVP of the fractional constant order. Further, two fixed point theorems due to Schauder and Banach are used and, finally, the Ulam-Hyers-Rassias stability of the given variable order Hadamard FBVP is examined. These results are supported with the aid of a comprehensive example. [ABSTRACT FROM AUTHOR]

Our basic purpose is to derive several existence aspects of solutions for a novel class of the fractional inclusion problem in terms of the well-defined generalized φ-Caputo and φ-Riemann–Liouville operators. The existing boundary conditions in such an inclusion problem are endowed with mixed generalized φ-Riemann–Liouville conditions. To reach this goal, we utilize the analytical methods on α-ψ-contractive maps and multifunctions involving approximate endpoint specification to derive the required results. In the final part, we formulate an illustrative simulation example to examine obtained theoretical outcomes by computationally and numerically. [ABSTRACT FROM AUTHOR]

In this research, we first investigate the existence of solutions for a new fractional boundary value problem in the Liouville–Caputo setting with mixed integro-derivative boundary conditions. To do this, Kuratowski's measure of noncompactness and Sadovskii's fixed point theorem are our tools to reach this aim. In the sequel, we discuss the continuous dependence of solutions on parameters by means of the generalized Gronwall inequality. Moreover, we consider an inclusion version of the given boundary problem in which we study its existence results by means of the endpoint theory. Finally, we prepare two simulative numerical examples to confirm the validity of the analytical findings. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and stability of solutions in connection to a non-local multiterm boundary value problem (BVP) with differential equations equipped with the Riemann-Liouville (RL) fractional derivative in the sense of Atangana-Baleanu of variable-order. The results about the existence property are investigated and proved via Krasnoselskii's fixed point theorem. Note that all theorems in the present research are studied based on piece-wise constant functions defined on generalized intervals. We shall convert our main BVP with the RL-fractional derivative of the Atangana-Baleanu type of variable-order to an equivalent BVP of constant order of the RL-Atangana-Baleanu derivative. In the next step, we examine the Ulam-Hyers stability for the supposed variable-order RL-Atangana-Baleanu BVP. Finally, we provide some examples to validate that our results are applicable. [ABSTRACT FROM AUTHOR]

In this research paper, we introduce a general structure of a fractional boundary value problem in which a 2-term fractional differential equation has a fractional bi-order setting of Riemann–Liouville type. Moreover, we consider the boundary conditions of the proposed problem as mixed Riemann–Liouville integro-derivative conditions with four different orders which cover many special cases studied before. In the first step, we investigate the existence and uniqueness of solutions for the given multi-order boundary value problem, and then the Hyers–Ulam stability is another notion in this regard which we study. Finally, we provide two illustrative examples to support our theoretical findings. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to concern with a new category of the sequential hybrid inclusion boundary value problem with three-point integro-derivative boundary conditions. In this direction, we employ various novel analytical techniques based on α-ψ-contractive mappings, endpoints, and the fixed points of the product operators to obtain the main results. Finally, we provide two examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated some topological properties of sets in a given gradual normed space. We have stated gradual Hausdor property and then, we have studied the relationship between gradual closed sets and gradual compact sets. Also, we have given a result about having the closure point for an infinite set in a gradual normed space. In the end, we have provided some illustrative examples. [ABSTRACT FROM AUTHOR]

• Fractional control law for the Stanford robot for tracking trajectory tasks is proposed. • Coupled system is composed of the robot manipulator and the actuators of the joints consider induction motors. • Dynamics of the system are obtained by the Euler–Lagrange method and generalized through the Caputo Fabrizio derivative. • Fractional integral sliding mode control via the Caputo–Fabrizio derivative for trajectory tracking control. • Introduction of AB- integral in the fractional sliding surface improving controller performance. In this work, a fractional integral sliding-mode control scheme based on the Caputo–Fabrizio derivative and the Atangana–Baleanu integral of the Stanford robot for trajectory tracking tasks is developed and presented. The coupled system is composed of the robot manipulator and the induction motors that drive its joints. The mathematical model of the system is obtained by the Euler–Lagrange method and generalized to an arbitrary order via the Caputo–Fabrizio derivative. The actuators are controlled by fractional PI controllers based on the Atangana–Baleanu integral, while a fractional integral sliding mode control law is also developed for trajectory tracking control. In this context, a fractional version of the sliding surface via the Caputo–Fabrizio derivative is introduced to improve the performance of the control system. In addition, to attenuate the chattering effects, a fractional integral term, based on the Atangana–Baleanu integral, is introduced on the sliding surface further improving system performance with less power consumption. The conventional integral sliding mode control and an optimal super-twisting sliding mode control are also introduced for comparison with the proposed control strategy. The control schemes were tuned using the Cuckoo method. External disturbances are also considered in the system dynamics, as well as different end-effector reference trajectories, which were designed to carry out manufacturing tasks. Simulation results confirm the superiority of our control scheme for trajectory-tracking applications over its conventional version and the optimal super-twisting sliding mode control, even with external disturbances and trajectory changes. To show the robustness of the proposed control scheme under different operating conditions, all the numerical simulations were performed considering the same orders and gains. Finally, our control law introduces the fractional derivative and integral of Caputo–Fabrizio and Atangana–Baleanu respectively, which have not been used enough in the modeling and control of robotic systems. Therefore, it is interesting to analyze the contributions and advantages that arise when using them. [ABSTRACT FROM AUTHOR]

The development of laser‐based cooling and spectroscopic methods has produced unprecedented growth in the ion trapping industry. Mathieu equation, a differential equation with periodic coefficients, is employed to develop models of ion motions under the influence of fields. Ion traps with octopole field is described with nonlinear Mathieu equation with cubic term. This article aims at considering motion of ions under the electric potential with negative octopole field with damping caused by the collision of the ions with Helium buffer gas modeled with tempered fractional derivative. Schaefer's fixed point theorem and Banach's contraction principle are employed to establish the existence of unique solution for the considered tempered fractional nonlinear Mathieu equation model of an ion motion. Further, the analysis of stability is performed in the sense of Hyers and Ulam. The feasibility of the obtained theoretical results are numerically confirmed for suitable parametric values, and simulations are performed supporting them. [ABSTRACT FROM AUTHOR]

Waterborne diseases are illnesses caused by pathogenic bacteria that spread through water and have a negative influence on human health. Due to the involvement of most countries in this vital issue, accurate analysis of mathematical models of such diseases is one of the first priorities of researchers. In this regard, in this paper, we turn to a waterborne disease model for solution's existence, HU-stability, and computational analysis. We transform the model to an analogous fractal-fractional integral form and study its qualitative analysis using an iterative convergent sequence and fixed-point technique to see whether there is a solution. We use Lagrange's interpolation to construct numerical algorithms for the fractal-fractional waterborne disease model in terms of computations. The approach is then put to the test in a case study, yielding some interesting outcomes. [ABSTRACT FROM AUTHOR]

In this manuscript, we study the existence and uniqueness of solutions for a new neutral hybrid nonlinear differential equation in the context of a fractional generalized operator in the sense of ψ-Caputo. To emphasize the novelty of the manuscript, a pure technique of the noncompactness measures is applied to a hybrid system based on the notion of the modulus of continuity in Darbo's criterion that covers the existing results of other works published before. The Ulam–Hyers and generalized Ulam–Hyers stabilities are explored for the given neutral nonhybrid nonlinear problem. An application is prepared in the framework of an example to ensure the validity of theorems for different cases. [ABSTRACT FROM AUTHOR]

This study deals with a novel class of mean-type inequalities by employing fractional calculus and convexity theory. The high correlation between symmetry and convexity increases its significance. In this paper, we first establish an identity that is crucial in investigating fractional mean inequalities. Then, we establish the main results involving the error estimation of the Hermite–Hadamard inequality for composite convex functions via a generalized Riemann-type fractional integral. Such results are verified by choosing certain composite functions. These results give well-known examples in special cases. The main consequences can generalize many known inequalities that exist in other studies. [ABSTRACT FROM AUTHOR]

In this paper, we first establish two quantum integral (q-integral) identities with the help of derivatives and integrals of the quantum types. Then, we prove some new q-midpoint and q-trapezoidal estimates for the newly established q-Hermite-Hadamard inequality (involving left and right integrals proved by Bermudo et al.) under q-differentiable convex functions. Finally, we provide some examples to illustrate the validity of newly obtained quantum inequalities. [ABSTRACT FROM AUTHOR]

Drugs have always been one of the most important concerns of families and government officials at all times, and they have caused irreparable damage to the health of young people. Given the importance of this great challenge, this article discusses a non-symmetric fractal-fractional order ice-smoking mathematical model for the existence results, numerical results, and stability analysis. For the existence of the solution of the given ice-smoking model, successive iterative sequences are defined. The uniqueness of the solution Hyers–Ulam (HU) stability is established with the help of the existing definitions and theorems in functional analysis. By the utilization of two-step Lagrange polynomials, we provide numerical solutions and provide a comparative numerical analysis for different values of the fractional order and fractal order. The numerical simulations show the applicability of the scheme and future prediction and the effects of fractal-fractional orders simultaneously. [ABSTRACT FROM AUTHOR]

In this article, we provide constraints for the sum by employing a generalized modified form of fractional integrals of Riemann-type via convex functions. The mean fractional inequalities for functions with convex absolute value derivatives are discovered. Hermite–Hadamard-type fractional inequalities for a symmetric convex function are explored. These results are achieved using a fresh and innovative methodology for the modified form of generalized fractional integrals. Some applications for the results explored in the paper are briefly reviewed. [ABSTRACT FROM AUTHOR]

In this paper, we conduct a research on a new version of the (p , q) -Hermite–Hadamard inequality for convex functions in the framework of postquantum calculus. Moreover, we derive several estimates for (p , q) -midpoint and (p , q) -trapezoidal inequalities for special (p , q) -differentiable functions by using the notions of left and right (p , q) -derivatives. Our newly obtained inequalities are extensions of some existing inequalities in other studies. Lastly, we consider some mathematical examples for some (p , q) -functions to confirm the correctness of newly established results. [ABSTRACT FROM AUTHOR]

In both pure and applied mathematics, convex functions are used in many different problems. They are crucial to investigate both linear and non-linear programming issues. Since a convex function is one whose epigraph is a convex set, the theory of convex functions falls under the umbrella of convexity. However, it is a significant theory that affects practically all areas of mathematics. In this paper, we introduce the notions of g , h -convexity or convexity with respect to a pair of functions on co-ordinates and discuss its fundamental properties. Moreover, we establish some novel Hermite–Hadamard- and Ostrowski-type inequalities for newly introduced co-ordinated convexity. Additionally, it is presented that the newly introduced notion of the convexity and given inequalities are generalizations of existing studies in the literature. Lastly, we look at various mathematical examples and graphs to confirm the validity of the newly found inequalities. [ABSTRACT FROM AUTHOR]

The existence of solutions for a coupled system of time-fractional differential equations including continuous functions and the Caputo-Fabrizio fractional derivative is examined. After that we investigated a coupled system of time-fractional differential inclusions including compact- and convex-valued L1-Caratheodory multifunctions and the Caputo-Fabrizio fractional derivative. [ABSTRACT FROM AUTHOR]

In this paper, we study a new class of non-hybrid single-valued fractional boundary value problems equipped with integro-non-hybrid-multiterm-multipoint-multistrip conditions and a fully hybrid integro-multi-valued fractional boundary value problem by some new methods including the Kuratowski measures based on Sadovskii's theorem, Krasnoselskii–Zabreiko criterion, and Dhage's technique. We generalize the Gronwall inequality in relation to a non-hybrid single-valued fractional boundary value problem, and then we investigate the stability notions in two versions. To examine the correctness of the results, we provide some examples. [ABSTRACT FROM AUTHOR]

Cartilage regeneration/reconstruct is a noticeable challenge in cartilage tissue engineering. In this study, through electrospinning technique, poly(caprolactone) (PCL), gelatin (Gel) and casein (Cas) were used to fabricate electrospun scaffold for cartilage tissue engineering applications. The physicochemical properties of fabricated scaffolds were assessed by scanning electron microscopy (SEM), water contact angle (WCA), mechanical assessment, water uptake measurement and in-vitro degradation assay. The cell/scaffold interactions were assessed through MTT assay and SEM observation. The obtained results showed the uniform and bead-free PCL/Gel/Cas fibres produced with a mean diameter of about 259.27 ± 56.33 nm, and 15.98 ± 2.14 µm pore size. The tensile assessment revealed that PCL/Gel fibres with 2 wt% Cas reached 9.8 ± 1.6 MPa. The MTT assay also showed that PCL/Gel fibres with 2 wt% Cas had proper cell viability and proliferation comparable with PCL/Gel scaffold. It can be concluded that the PCL/Gel/Cas nanofibrous scaffold can be a desirable candidate for cartilage tissue engineering. [ABSTRACT FROM AUTHOR]

The existence and the uniqueness theorems play a crucial role prior to finding the numerical solutions of the fractional differential equations describing the models corresponding to the real world applications. In this paper, we study the existence of solutions for a time-fractional integrodifferential equation via three-point boundary value conditions. [ABSTRACT FROM AUTHOR]

The existence aspects along with the stability of solutions to a Hadamard variable order fractional boundary value problem are investigated in this research study. Our results are obtained via generalized intervals and piecewise constant functions and the relevant Green function, by converting the existing Hadamard variable order fractional boundary value problem to an equivalent standard Hadamard fractional boundary problem of the fractional constant order. Further, Darbo's fixed point criterion along with Kuratowski's measure of noncompactness is used in this direction. As well as, the Ulam-Hyers-Rassias stability of the proposed Hadamard variable order fractional boundary value problem is established. A numerical example is presented to express our results' validity. [ABSTRACT FROM AUTHOR]

In this study, we introduced a novel scheme to attain approximate and closed-form solutions of conformable Newell-Whitehead-Segel (NWS) equations, which belong to the most consequential amplitude equations in physics. The conformable Shehu transform (CST) and the Adomian decomposition method (ADM) are combined in the proposed method. We call it the conformable Shehu decomposition method (CSDM). To assess the efficiency and consistency of the recommended method, we demonstrate 2D and 3D graphs as well as numerical simulations of the derived solutions. As a result, CSDM demonstrates that it is a useful and simple mathematical tool for getting approximate and exact analytical solutions to linear-nonlinear fractional partial differential equations (PDEs) of the given kind. The convergence and absolute error analysis of the series solutions is also offered. [ABSTRACT FROM AUTHOR]

In the current manuscript, we intend to investigate the existence, uniqueness, and the stability of positive solution in relation to a fractional version of variable order thermostat model equipped with nonlocal boundary values in the Caputo sense. In fact, we will get help from the constant piece-wise functions for transforming our variable order model into an auxiliary standard model of thermostat. By Guo-Krasnoselskii's fixed point theorem on cones, we derive the required conditions ensuring the existence property for positive solutions. An example is illustrated to examine the validity of the observed results. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has caused emotional loss to people around the world and provides an unusual test for public welfare, educational framework, food frameworks, and the world of work. The economic and social turmoil caused by this epidemic is increasing, and many people are at risk of falling into oppressive poverty. In this article, we describe the pandemic of infectious illness with the help of stochastic mathematical modeling. Based on the environmental white noise and by building appropriate Lyapunov functions and by applying Ito's formula, a few subjective properties are gotten. We provide a new mathematical model for the COVID-19 spread. The novel stochastic model is used to analyze the existence and prevalence of the disease, as well as its extinction. A numerical approach is developed for computing approximate solutions of the model. We show numerical simulations of deterministic and stochastic models of COVID-19 by utilizing the MATLAB software. In this direction, three graphs are included in the paper for the numerical interpretation of the stochastic model with the help of existing parametric and initial values for the model. [ABSTRACT FROM AUTHOR]

This work is reserved for the study of a special category of boundary value problems (BVP s) consisting of Liouville–Caputo integro-differential equations with multiple nonlinear terms. This fractional model and its boundary value conditions (BVCs) involve different simple BVP s, in which the second BVC as a linear combination of two Caputo derivatives of the unknown function equals a nonzero constant. The Banach principle gives a unique solution for this Liouville–Caputo BVP. Further, the Krasnoselskii and Leray–Schauder criteria give the existence property regarding solutions of the mentioned problem. For each theorem, we provide an example based on the required hypotheses and derive numerical data in the framework of tables and figures to show the consistency of results from different points of view. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of solutions to a nonlinear boundary value problem (BVP) of variable order at resonance. The main theorem in this study is proved with the help of generalized intervals and piecewise constant functions, in which we convert the mentioned Caputo BVP of fractional variable order to an equivalent standard Caputo BVP at resonance of constant order. In fact, to use the Mawhin's continuation technique, we have to transform the variable order BVP into a constant order BVP. We prove the existence of solutions based on the existing notions in the coincidence degree theory and Mawhin's continuation theorem (MCTH). Finally, an example is provided according to the given variable order BVP to show the correctness of results. [ABSTRACT FROM AUTHOR]

In this paper, a newfangled technique for edge detection that combines the Khalil conformable derivative and the Hessian matrix is developed and experimentally validated. The following main aspects are considered: (i) to attenuate image noise a Gaussian kernel inspired by the Khalil conformable derivative was developed. (ii) The spatial derivatives of the image gray level are calculated via the Khalil derivative, which is suitable for maintaining object contours and texture information even in low-contrast and resolution images. (iii) The conformable Hessian matrix is obtained from these image derivatives, generating continuous, thicker, and brighter edges. Our operator is compared with some existing techniques. Simulation results on different test images confirm a greater robustness to noise by our operator as well as a better visual quality of the edge maps obtained. This statement is validated through a comparative analysis based on peak signal-to-noise ratio and edge-strength-similarity-based image quality. In addition, it is applied in medical image processing and analysis tasks such as mammogram images, computed tomography scans, and magnetic resonance imaging for identification tasks of middle cerebral artery aneurysms, calcifications and breast cancer, proliferative Diabetic Retinopathy, and cerebral arteriovenous malformations. According to our findings, the conformable operator allows better visual identification of the structure of these conditions, improving the accuracy of clinical diagnosis and its subsequent monitoring. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to investigate the existence, uniqueness, and Ulam–Hyers stability of positive solutions for fractional integro-differential boundary values problem. Uniqueness result is obtained by using the Banach principle. For obtaining two positive solutions, we apply another fixed point criterion due to Avery–Anderson–Henderson on cones by establishing some inequalities. An illustrative example is presented to indicate the validity of the obtained results. The results are new and provide a generalization to some known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for a generalized sequential Caputo-type fractional neutral differential inclusion with generalized integral conditions. The used fractional operator has the generalized kernel in the format of (ϑ (t) − ϑ (s)) along with differential operator 1 ϑ ′ (t) d d t . We obtain existence results for two cases of convex-valued and nonconvex-valued multifunctions in two separated sections. We derive our findings by means of the fixed point principles in the context of the set-valued analysis. We give two suitable examples to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this research work, a newly-proposed multiterm hybrid multi-order fractional boundary value problem is studied. The existence results for the supposed hybrid fractional differential equation that involves Riemann–Liouville fractional derivatives and integrals of multi-orders type are derived using Dhage's technique, which deals with a composition of three operators. After that, its stability analysis of Ulam–Hyers type and the relevant generalizations are checked. Some illustrative numerical examples are provided at the end to illustrate and validate our obtained results. [ABSTRACT FROM AUTHOR]

In this work, we study the existence, uniqueness, and continuous dependence of solutions for a class of fractional differential equations by using a generalized Riesz fractional operator. One can view the results of this work as a refinement for the existence theory of fractional differential equations with Riemann–Liouville, Caputo, and classical Riesz derivative. Some special cases can be derived to obtain corresponding existence results for fractional differential equations. We provide an illustrated example for the unique solution of our main result. [ABSTRACT FROM AUTHOR]

In this paper, a new class of a neutral functional delay differential equation involving the generalized ψ -Caputo derivative is investigated on a partially ordered Banach space. The existence and uniqueness results to the given boundary value problem are established with the help of the Dhage's technique and Banach contraction principle. Also, we prove other existence criteria by means of the topological degree method. Finally, Ulam-Hyers type stability and its generalized version are studied. Two illustrative examples are presented to demonstrate the validity of our obtained results. [ABSTRACT FROM AUTHOR]

In this research study, we are concerned with the existence and stability of solutions of a boundary value problem (BVP) of the fractional thermostat control model with ψ-Hilfer fractional operator. We verify the uniqueness criterion via the Banach fixed-point principle and establish the existence by using the Schaefer and Krasnoselskii fixed-point results. Moreover, we apply the arguments related to the nonlinear functional analysis to discuss various types of stability in the format of Ulam. Finally, by several examples we demonstrate applications of the main findings. [ABSTRACT FROM AUTHOR]

The main intention of this article is that new techniques of existence theory are used to derive some required criteria pertinent to a given fractional multi-term problem and its inclusion version. In such an approach, we do our research on a fractional integral equation corresponding to the mentioned BVPs. In more precise words, by virtue of this integral equation, we construct new operators which belong to a special category of functions named α-admissible and α-ψ-contraction maps coupled with operators having (AEP)-property. Next, by considering some new properties on the existing Banach space having properties (B) and (C α) , our argument for ensuring the existence of solutions is completed. In addition, we also add two simulative examples to review our findings by a numerical view. [ABSTRACT FROM AUTHOR]

In this research article, we turn to studying the existence and different types of stability such as generalized Ulam–Hyers stability and generalized Ulam–Hyers–Rassias stability of solutions for a new modeling of a boundary value problem equipped with the fractional differential equation which contains the multi-order generalized Caputo type derivatives furnished with four-point mixed generalized Riemann–Liouville type integro-derivative conditions. At the end of the current paper, we formulate two illustrative examples to confirm the correctness of theoretical findings from computational aspects. [ABSTRACT FROM AUTHOR]

In the present research manuscript, we formulate a new generalized structure of the nonlinear Caputo fractional quantum multi-integro-differential equation in which such a multi-order structure of quantum integrals is considered for the first time. In fact, in the light of this type of boundary value problem equipped with the multi-integro-differential setting, one can simply study different cases of the existing usual integro-differential problems in the literature. In this direction, we utilize well-known analytical techniques to derive desired criteria which guarantee the existence of solutions for the proposed multi-order quantum multi-integro-differential problem. Further, some numerical examples are considered to examine our theoretical and analytical findings using the proposed methods. [ABSTRACT FROM AUTHOR]

In the present research article, we find some important criteria on the existence of solutions for a class of the hybrid fractional Caputo–Hadamard differential equations and its corresponding inclusion problem supplemented with hybrid Hadamard integral boundary conditions. In this direction, we utilize some theorems due to Dhage's fixed point results in our proofs. Finally, we demonstrate two numerical examples to confirm the validity of the main obtained results. [ABSTRACT FROM AUTHOR]

The original article can be found online at https://doi.org/10.1186/s13662-021-03459-w Correction: Advances in Difference Equations (2021) 2021:303 https://doi.org/10.1186/s13662-021-03459-w Following publication of the original article [[1]], the authors reported an error in the first author name, the correct author name is Muhammad Aleem. Correction: on solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz-Caputo operator Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. [Extracted from the article]

Few studies have investigated the existence and uniqueness of solutions for fractional differential equations on star graphs until now. The published papers on the topic are based on the assumption of existence of one junction node and some boundary nodes as the origin on a star graph. These structures are special cases and do not cover more general non-star graph structures. In this paper, we state a labeling method for graph vertices, and then we prove the existence results for solutions to a new family of fractional boundary value problems (FBVPs) on the methylpropane graph. We design the chemical compound of the methylpropane graph with vertices specified by 0 or 1, and on every edge of the graph, we consider fractional differential equations. We prove the existence of solutions for the proposed FBVPs by means of the Krasnoselskii's and Scheafer's fixed point theorems, and further, we study the Ulam–Hyers type stability for the given multi-dimensional system. Finally, we provide an illustrative example to examine our results. [ABSTRACT FROM AUTHOR]

This paper is devoted to generalizing the standard system of Navier boundary value problems to a fractional system of coupled sequential Navier boundary value problems by using terms of the Caputo derivatives. In other words, for the first time, we design a multi-term fractional coupled system of Navier equations under the fractional boundary conditions. The existence theory is studied regarding solutions of the given coupled sequential Navier boundary problems via the Krasnoselskii's fixed-point theorem on two nonlinear operators. Moreover, the Banach contraction principle is applied to investigate the uniqueness of solution. We then focus on the Hyers–Ulam-type stability of its solution. Furthermore, the approximate solutions of the proposed coupled fractional sequential Navier system are obtained via the generalized differential transform method. Lastly, the results of this research are supported by giving simulated examples. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel mathematical model for the spread of COVID-19 involving environmental white noise. The new stochastic model was studied for the existence and persistence of the disease, as well as the extinction of the disease. We noticed that the existence and extinction of the disease are dependent on R 0 (the reproduction number). Then, a numerical scheme was developed for the computational analysis of the model; with the existing values of the parameters in the literature, we obtained the related simulations, which gave us more realistic numerical data for the future prediction. The mentioned stochastic model was analyzed for different values of σ 1 , σ 2 and β 1 , β 2 , and both the stochastic and the deterministic models were compared for the future prediction of the spread of COVID-19. [ABSTRACT FROM AUTHOR]

Our main purpose in this paper is to prove the existence of solutions for the fractional strongly singular thermostat model under some generalized boundary conditions. In this way, we use some recent nonlinear fixed-point techniques involving α - ψ -contractions and α -admissible maps. Further, we establish the similar results for the hybrid version of the given fractional strongly singular thermostat control model. Some examples are studied to illustrate the consistency of our results. [ABSTRACT FROM AUTHOR]

In this paper, the existence of the solution and its stability to the fractional boundary value problem (FBVP) were investigated for an implicit nonlinear fractional differential equation (VOFDE) of variable order. All existence criteria of the solutions in our establishments were derived via Krasnoselskii's fixed point theorem and in the sequel, and its Ulam–Hyers–Rassias (U-H-R) stability is checked. An illustrative example is presented at the end of this paper to validate our findings. [ABSTRACT FROM AUTHOR]

We study a coupled system of implicit differential equations with fractional-order differential boundary conditions and the Riemann–Liouville derivative. The existence, uniqueness, and at least one solution are established by applying the Banach contraction and Leray–Schauder fixed point theorem. Furthermore, Hyers–Ulam type stabilities are discussed. An example is presented to illustrate our main result. The suggested system is the generalization of fourth-order ordinary differential equations with anti-periodic, classical, and initial boundary conditions. [ABSTRACT FROM AUTHOR]