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Fractional calculus provides some fractional operators for us to model different real-world phenomena mathematically. One of these important study fields is the mathematical model of the elastic beam changes. More precisely, in this paper, based on the behavior patterns of an elastic beam, we consider the generalized sequential boundary value problems of the Navier difference equations by using the post-quantum fractional derivatives of the Caputo-like type. We discuss on the existence theory for solutions of the mentioned (p ; q) -difference Navier problems in two single-valued and set-valued versions. We use the main properties of the (p ; q) -operators in this regard. Application of the fixed points of the ρ - θ -contractions along with the endpoints of the multi-valued functions play a fundamental role to prove the existence results. Finally in two examples, we validate our models and theoretical results by giving numerical models of the generalized sequential (p ; q) -difference Navier problems. [ABSTRACT FROM AUTHOR]

In this research study, we formulate two generalized nonlinear multi-order fractional boundary value problems with the help of quantum diffeerence operators. To investigate the exis- tence property for possible solutions of these q-di_erence FBVPs, we apply two separate methods motivated by some notions in relation to the measure of noncompactness and end-point technique. The condensing functions and multifunctions having the (AE)-property play an important role in our study. As well as, two examples corresponding to both techniques are provided to ensure the compatibility of the findings numerically. [ABSTRACT FROM AUTHOR]

In this paper, we study a coupled fully hybrid system of (k , Φ) –Hilfer fractional differential equations equipped with non-symmetric (k , Φ) –Riemann-Liouville (RL) integral conditions. To prove the existence and uniqueness results, we use the Krasnoselskii and Perov fixed-point theorems with Lipschitzian matrix in the context of a generalized Banach space (GBS). Moreover, the Ulam–Hyers (UH) stability of the solutions is discussed by using the Urs's method. Finally, an illustrated example is given to confirm the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, a new kind of mathematical modeling is studied by providing a five-compartmental system of differential equations with respect to new hybrid generalized fractal-fractional derivatives. For the first time, we design a model of giving up smoking to analyze its dynamical behaviors by considering two parameters of such generalized operators; i.e., fractal dimension and fractional order. We apply a special sub-category of increasing functions to investigate the existence of solutions. Uniqueness property is derived by a standard method based on the Lipschitz rule. After proving stability property, the equilibrium points are obtained and asymptotically stable solutions are studied. Finally, we illustrate all analytical results and findings via numerical algorithms and graphs obtained by Lagrangian piece-wise interpolation, and discuss all behaviors of the relevant solutions in the fractal-fractional system. [ABSTRACT FROM AUTHOR]

In this paper, a new structure of an applied model of thermostat is defined using the generalized ψ -operators with three-point boundary conditions. Some useful properties of the relevant Green's function are established, and based on these properties, the Lyapunov-type inequality is constructed for the given extended ψ -model thermostat with the help of Jensen's inequality. By defining mild solutions for such an extended system, the existence and non-existence conditions are discussed. [ABSTRACT FROM AUTHOR]

SARS-CoV-2 is a strain of the large coronavirus family that has led to COVID-19 disease. The virus has been one of the deadliest known viruses in the world to date. Rapid mutations and the creation of new strains cause researchers to focus on the dynamic behaviors of the virus and to analyze it accurately through clinical research and mathematical models. In this paper, from the point of view of mathematical modeling, we intend to focus on the dynamic behavior of the system and examine its analytical and numerical aspects in two different structures. In other words, by recalling newly formulated hybrid fractional-fractal operators, we present a fractal-fractional probability-based model of SARS-CoV-2 virus for the first time and extract its equivalent compact fractal-fractional IVP to investigate its existence and stability criteria. A type of special admissible contractions will help us in this regard. Moreover, based on the source data, we simulate our system according to algorithms derived by Adams-Bashforth method and explain the effects of variation of the dimension of fractal and fractional order on dynamics of solutions. Finally, we transform our fractal-fractional model into a Caputo probability-based model of SARS-CoV-2 to derive solutions via the operational matrix method under Taylor's basis. The numerical simulations show close behaviors for both of models. [ABSTRACT FROM AUTHOR]

Results reported in this paper establish the existence of solutions for a class of generalized fractional inclusions based on the Caputo–Hadamard jerk system. Under some inequalities between multi-functions and with the help of special contractions and admissible maps, we investigate the existence criteria. Fixed points and end points are key roles in this manuscript, and the approximate property for end points helps us to derive the desired result for existence theory. An example is prepared to demonstrate the consistency and correctness of analytical findings. [ABSTRACT FROM AUTHOR]

The most important objective of the present research is to establish some theoretical existence results on a novel combined configuration of a Caputo sequential inclusion problem and the hybrid integro-differential one in which the boundary conditions are also formulated as the hybrid multi-order integro-differential conditions. In this respect, firstly, some inequalities are proven in relation to the corresponding integral equation. Then, we employ some newly defined theoretical techniques with the help of the product operators on a Banach algebra and also with the aid of some special functions including α - ψ -contractions and α -admissible mappings to extract the existence criteria corresponding to the given mixed sequential hybrid BVPs. Some important useful properties such as the approximate endpoint property, (C α) -property, and the compactness play a key role in this regard. The final part of the manuscript is devoted to formulating and computing two applicable examples to guarantee the correctness of the obtained results. [ABSTRACT FROM AUTHOR]

In recent decades, AIDS has been one of the main challenges facing the medical community around the world. Due to the large human deaths of this disease, researchers have tried to study the dynamic behaviors of the infectious factor of this disease in the form of mathematical models in addition to clinical trials. In this paper, we study a new mathematical model in which the dynamics of CD 4 + T-cells under the effect of HIV-1 infection are investigated in the context of a generalized fractal-fractional structure for the first time. The kernel of these new fractal-fractional operators is of the generalized Mittag-Leffler type. From an analytical point of view, we first derive some results on the existence theory and then the uniqueness criterion. After that, the stability of the given fractal-fractional system is reviewed under four different cases. Next, from a numerical point of view, we obtain two numerical algorithms for approximating the solutions of the system via the Adams-Bashforth method and Newton polynomials method. We simulate our results via these two algorithms and compare both of them. The numerical results reveal some stability and a situation of lacking a visible order in the early days of the disease dynamics when one uses the Newton polynomial. [ABSTRACT FROM AUTHOR]

Our aim in the present research article is to discuss some existence aspects of solutions for two given fractional q‐sequential structures of an integro‐differential BVP in which the R.H.S. nonlinear term is regarded as two functions in both single‐valued and multivalued versions. In addition to this, we formulate the boundary conditions in the framework of the mixed q‐integro‐derivative conditions simultaneously. For such new fractional q‐sequential integro‐differential structures, we utilize suitable standard analytical methods attributed to Krasnoselskii on the sum of two operators. In the final stage, we design two simulative examples to check the consistency of findings in the context of the proposed techniques. [ABSTRACT FROM AUTHOR]

The Lorenz-Stenflo mathematical model describes a complex dynamical behavior related to atmospheric acoustic-gravity waves. In this study, qualitative analysis of the four-dimensional hyperchaotic Lorenz-Stenflo system via the Caputo fractional derivative is implemented. By using the Matignon stability criterion, the local stability analysis of the system showed that all the equilibrium points of the system are locally unstable. Calculation of the Lyapunov exponents along with the relevant bifurcation diagrams with respect to different fractional orders exposed the hyperchaotic dynamical behavior for the system. Bifurcation diagrams for all the four parameters in the system also showed the hyperchaotic nature of the Lorenz-Stenflo system. Different phase attractors of the system corresponding to different fractional derivatives and parameters are presented to specify the dynamical nature of the system. The Lorenz-Stenflo system showed sensitivity to initial conditions. The master and slave systems showed a strong correlation among themselves, as verified by graphs of time series solutions of the two systems. [ABSTRACT FROM AUTHOR]

The fundamental goal of the study under consideration is to establish some of the existence criteria needed for a particular fractional inclusion model of cantilever beam in the setting of quantum calculus using new arguments of existence theory. In this way, we investigate a fractional integral equation that corresponds to the aforementioned boundary value problem. In a more concrete sense, we design new multi-valued operators based on this integral equation, which belong to the certain subclasses of functions, called α-admissible and α-ψ-contractive multi-functions, in combination with the AEP-property. Also, we use some inequalities such as Ω-inequality and set-valued version inequalities. Moreover, we add a simulative example for a numerical analysis of our results obtained in this study. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new structure of the generalized multi-point thermostat control model motivated by its standard model. By presenting integral solution of this boundary problem, the existence property along with the uniqueness property are investigated by means of a special version of contractions named μ-φ-contractions and the Banach contraction principle. Then, on the given nonlinear generalized BVP of thermostat, the Bernstein polynomials are introduced and numerical solutions obtained by them are presented. At the end, three different structures of nonlinear thermostat models are designed and the results are examined. [ABSTRACT FROM AUTHOR]

A memristor is naturally a nonlinear and at the same time memory element that may substitute resistors for next-generation nonlinear computational circuits that can show complex behaviors including chaos. A four-dimensional memristor system with the Atangana–Baleanu fractional nonsingular operator in the sense of Caputo is investigated. The Banach fixed point theorem for contraction principle is used to verify the existence–uniqueness of the fractional representation of the given system. A newly developed numerical scheme for fractional-order systems introduced by Toufik and Atangana is utilized to obtain the phase portraits of the suggested system for different fractional derivative orders and different parameter values of the system. Analysis on the local stability of the fractional model via the Matignon criteria showed that the trivial equilibrium point is unstable. The dynamics of the system are investigated using Lyapunov exponents for the characterization of the nature of the chaos and to verify the dissipativity of the system. It is shown that the supposed system is chaotic and it is significantly sensitive to parameter variation and small initial condition changes. [ABSTRACT FROM AUTHOR]

In this paper, we consider a new coupled system of fractional boundary value problems based on the thermostat control model. With the help of fixed point theory, we investigate the existence criterion of the solution to the given coupled system. This property is proved by using the Krasnoselskii's fixed point theorem and its uniqueness is proved via the Banach principle for contractions. Further, the Hyers–Ulam stability of solutions is investigated. Then, we find the approximate solution of the coupled fractional thermostat control system by using a numerical technique called the generalized differential transform method. To show the consistency and validity of our theoretical results, we provide two illustrative examples. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear sequential q-difference equation based on the Caputo fractional quantum derivatives with nonlocal boundary value conditions containing Riemann–Liouville fractional quantum integrals in four points. In this direction, we derive some criteria and conditions of the existence and uniqueness of solutions to a given Caputo fractional q-difference boundary value problem. Some pure techniques based on condensing operators and Sadovskii's measure and the eigenvalue of an operator are employed to prove the main results. Also, the Ulam–Hyers stability and generalized Ulam–Hyers stability are investigated. We examine our results by providing two illustrative examples. [ABSTRACT FROM AUTHOR]

In the present research study, for a given multiterm boundary value problem (BVP) involving the nonlinear fractional differential equation (NnLFDEq) of variable order, the uniqueness-existence properties are analyzed. To arrive at such an aim, we first investigate some specifications of this kind of variable order operator and then derive required criteria confirming the existence of solution. All results in this study are established with the help of two fixed-point theorems and examined by a practical example. [ABSTRACT FROM AUTHOR]

In the current research, we derive some existence and stability criteria for two hybrid and non‐hybrid differential equations of fractional order. By utilizing an analytical technique based on the generalized Dhage's fixed point result, we verify desired existence theorem for the hybrid problem. Also, we consider a special case as a non‐hybrid problem and by using the Kuratowski's measure of non‐compactness, we establish a new existence criterion. Eventually, we turn to investigation of the stability of solutions for the non‐hybrid problem by applying the generalized Gronwall's inequality. Finally, we provide an example to illustrate the relevant non‐hybrid result. [ABSTRACT FROM AUTHOR]

The present research work investigates some new results for a fractional generalized Sturm–Liouville–Langevin (FGSLL) equation involving the Ψ-Caputo fractional derivative with a modified argument. We prove the uniqueness of the solution using the Banach contraction principle endowed with a norm of the Ψ-Bielecki-type. Meanwhile, the fixed-point theorems of the Leray–Schauder and Krasnoselskii type associated with the Ψ-Bielecki-type norm are used to derive the existence properties by removing some strong conditions. We use the generalized Gronwall-type inequality to discuss Ulam–Hyers (UH), generalized Ulam–Hyers (GUH), Ulam–Hyers–Rassias (UHR), and generalized Ulam–Hyers–Rassias (GUHR) stability of these solutions. Lastly, three examples are provided to show the effectiveness of our main results for different cases of (FGSLL)-problem such as Caputo-type Sturm–Liouville, Caputo-type Langevin, Caputo–Erdélyi–Kober-type Langevin problems. [ABSTRACT FROM AUTHOR]

A class of the boundary value problem is investigated in this research work to prove the existence of solutions for the neutral fractional differential inclusions of Katugampola fractional derivative which involves retarded and advanced arguments. New results are obtained in this paper based on the Kuratowski measure of noncompactness for the suggested inclusion neutral system for the first time. On the one hand, this research concerns the set-valued analogue of Mönch fixed point theorem combined with the measure of noncompactness technique in which the right-hand side is convex valued. On the other hand, the nonconvex case is discussed via Covitz and Nadler fixed point theorem. An illustrative example is provided to apply and validate our obtained results. [ABSTRACT FROM AUTHOR]

Our fundamental purpose in the present manuscript is to explore existence and uniqueness criteria for a new coupled Caputo conformable system of pantograph problems in which for the first time, the given boundary conditions are formulated in the Riemann-Liouville conformable framework. To reach the mentioned aims, we utilize different analytical techniques in which some fixed point results play a vital role. In the final part, a simulative example is designed to cover the applicability aspects of theoretical findings available in this research manuscript from a numerical point of view. [ABSTRACT FROM AUTHOR]

In the present research manuscript, we introduce a novel general fractional boundary value inclusion problem and investigate the necessary and sufficient conditions for desired existence results. Indeed, more precisely, we formulate a class of fractional multiterm Caputo–Hadamard differential inclusion problem with two‐point sum boundary value conditions. In two separate theorems, we prove the existence results for mentioned inclusion problem by using α‐ψ‐contractive maps and approximate endpoint property. Finally, we provide an example to illustrate our main results. [ABSTRACT FROM AUTHOR]

We study two hybrid and non-hybrid fractional boundary value problems via the Caputo–Hadamard type derivatives. We seek the existence criteria for these two problems separately. By utilizing the generalized Dhage's theorem, we derive desired results for an integral structure of solutions for the hybrid problems. Also by considering the special case as a non-hybrid boundary value problem (BVP), we establish other results based on the existing tools in the topological degree theory. In the end of the article, we examine our theoretical results by presenting some numerical examples to show the applicability of the analytical findings. [ABSTRACT FROM AUTHOR]

A few researchers have studied fractional differential equations on star graphs. They use star graphs because their method needs a common point which has edges with other nodes while other nodes have no edges between themselves. It is natural that we feel that this method is incomplete. Our aim is extending the method on more generalized graphs. In this work, we investigate the existence of solutions for some fractional boundary value problems on the ethane graph. In this way, we consider a graph with labeled vertices by 0 or 1, inspired by a graph representation of the chemical compound of ethane, and define fractional differential equations on each edge of this graph. Also, we provide an example to illustrate our last main result. [ABSTRACT FROM AUTHOR]

We investigate the existence of solutions for a Caputo–Hadamard fractional integro-differential equation with boundary value conditions involving the Hadamard fractional operators via different orders. By using the Krasnoselskii's fixed point theorem, the Leray–Schauder nonlinear alternative, and the Banach contraction principle, we prove our main results. Also, we provide three examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

We investigate the existence of solutions for a fractional hybrid multi-term integro-differential inclusion with four-point sum and integral boundary value conditions. By using Dhage's fixed point results, we prove our main existence result. Finally, we give an example to illustrate our main result. [ABSTRACT FROM AUTHOR]

We review the existence of solutions for a three-point nonlinear q-fractional differential equation and also its related inclusion. In this way, we use α-ψ-contractions and multifunctions. Also, we provide two examples to illustrate our main results. Finally by providing some algorithms and tables, we give some numerical computations for the results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of solutions for two nonlinear fractional multi-term integro-differential inclusions in two hybrid and non-hybrid versions. The boundary value conditions are in the form of three-point integral hybrid conditions. In this way, we define a new operator based on the integral solution of the given boundary value inclusion problem and then we use assumptions of a Dhage's fixed point result for this fractional operator in the hybrid case. Also, the approximate endpoint property is applied for the corresponding set-valued maps in the non-hybrid case. Finally, we provide two examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

We provide an extension for the second-order differential equation of a thermostat model to the fractional hybrid equation and inclusion versions. We consider boundary value conditions of this problem in the form of the hybrid conditions. To prove the existence of solutions for our hybrid fractional thermostat equation and inclusion versions, we apply the well-known Dhage fixed point theorems for single-valued and set-valued maps. Finally, we give two examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we derive a Mittag-Leffler function for real index and establish solutions of special type of fractional order differential equations (FDEs). The same concept is extended to discrete case by replacing polynomials into factorial polynomials and differentiation into l-difference operator. Moreover, numerical examples of our results are stated to validate our findings. The acquired results here have the ability to generate a wide range of formulas in relation to newer results. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for a new class of boundary value problems for nonlinear multi-term fractional differential inclusions. Our main result relies on the multi-valued form of Krasnoselskii's fixed point theorem. An illustrative example is also presented. [ABSTRACT FROM AUTHOR]

In this paper, by using the endpoint result for multifunctions, we investigate the existence of solutions for a boundary value problem for fractional differential inclusions with sum and integral boundary conditions. Finally, an example is also given to illustrate the validity of our main result. [ABSTRACT FROM AUTHOR]

This paper derives some equalities via twice differentiable functions and conformable fractional integrals. With the help of the obtained identities, we present new trapezoid-type and midpoint-type inequalities via convex functions in the context of the conformable fractional integrals. New inequalities are obtained by taking advantage of the convexity property, power mean inequality, and Hölder's inequality. We show that this new family of inequalities generalizes some previous research studies by special choices. Furthermore, new other relevant results with trapezoid-type and midpoint-type inequalities are obtained. [ABSTRACT FROM AUTHOR]

In the current paper, we intend to check the existence aspects of solutions for a category of the multi‐point boundary value problem (BVP) involving a p$$ p $$‐Laplacian differential operator within the generalized fractional derivatives depending on another function. Based on two fixed point results attributed to Schaefer and Banach, the desired results are verified. Further, the continuity of solutions in terms of inputs (fractional orders, associated parameters, and appropriate function) is extensively discussed. A simulative example is prepared to demonstrate the applications of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for a new class of boundary value problems for nonlinear fractional differential inclusions with mixed type integral boundary conditions. The cases when the multifunction has convex as well as non-convex values are considered. Our results rely on the standard tools of fixed point theory and are well illustrated with the aid of an example. [ABSTRACT FROM AUTHOR]

The aim of this study is to provide a generalization of prime vague Γ -ideals in Γ -rings by introducing non-symmetric 2-absorbing vague weakly complete Γ -ideals of commutative Γ -rings. A novel algebraic structure of a primary vague Γ -ideal of a commutative Γ -ring is presented by 2-absorbing weakly complete primary ideal theory. The approach of non-symmetric 2-absorbing K-vague Γ -ideals of Γ -rings are examined and the relation between a level subset of 2-absorbing vague weakly complete Γ -ideals and 2-absorbing Γ -ideals is given. The image and inverse image of a 2-absorbing vague weakly complete Γ -ideal of a Γ -ring and 2-absorbing K-vague Γ -ideal of a Γ -ring are studied and a 1-1 inclusion-preserving correspondence theorem is given. A vague quotient Γ -ring of R induced by a 2-absorbing vague weakly complete Γ -ideal of a 2-absorbing Γ -ring is characterized, and a diagram is obtained that shows the relationship between these concepts with a 2-absorbing Γ -ideal. [ABSTRACT FROM AUTHOR]

In this paper, a tripled fractional differential system is introduced as three associated impulsive equations. The existence investigation of the solution is based on contraction principle and measures of noncompactness in terms of tripled fixed point and modulus of continuity. Our results are valid for both Kuratowski and Hausdorff measures of noncompactness. As an application, we apply the obtained results to a control problem. [ABSTRACT FROM AUTHOR]

In this paper, we establish several necessary conditions to confirm the uniqueness-existence of solutions to an extended multi-order finite-term fractional differential equation with double-order integral boundary conditions with respect to asymmetric operators by relying on the Banach's fixed-point criterion. We validate our study by implementing two numerical schemes to handle some Riemann–Liouville fractional boundary value problems and obtain approximate series solutions that converge to the exact ones. In particular, we present several examples that illustrate the closeness of the approximate solutions to the exact solutions. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions and their uniqueness and different kinds of Ulam–Hyers stability for a new class of nonlinear Caputo quantum boundary value problems. Also, we investigate such properties for the relevant generalized coupled q -system involving fractional quantum operators. By using the Banach contraction principle and Leray-Schauder's fixed–point theorem, we prove the existence and uniqueness of solutions for the suggested fractional quantum problems. The Ulam–Hyers stability of solutions in different forms are studied. Finally, some examples are provided for both q -problem and coupled q -system to show the validity of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we provide some appropriate conditions for the existence of solutions for a perturbed fractional neutral integro-differential system under the deformable derivative in a Banach space. Using the Banach contraction principle and Krasnoselskii's fixed point theorem, we establish some new existence theorems. Moreover, we provide two numerical examples to demonstrate the applicability of the theoretical results [ABSTRACT FROM AUTHOR]

In this research, we introduce a new and generalized family of convex functions, entitled the α-convex functions in the second sense with respect to a parameter and examine their important algebraic properties. Based on this novel convexity concept, we explore a new class of fractional integral inequalities for functions that are twice differentiable. These results are derived from fundamental identities obtained using classical Riemann–Liouville fractional integrals. To validate our findings, we provide 2D and 3D graphs of the main results. Furthermore, as an additional aspect of our study, we explore error estimates for differences of generalized means. [ABSTRACT FROM AUTHOR]

In this research study, we establish some necessary conditions to check the uniqueness-existence of solutions for a general multi-term ψ -fractional differential equation via generalized ψ -integral boundary conditions with respect to the generalized asymmetric operators. To arrive at such purpose, we utilize a procedure based on the fixed-point theory. We follow our study by suggesting two numerical algorithms called the Dafterdar-Gejji and Jafari method (DGJIM) and the Adomian decomposition method (ADM) techniques in which a series of approximate solutions converge to the exact ones of the given ψ -RLFBVP and the equivalent ψ -integral equation. To emphasize for the compatibility and the effectiveness of these numerical algorithms, we end this investigation by providing some examples showing the behavior of the exact solution of the existing ψ -RLFBVP compared with the approximate ones caused by DGJIM and ADM techniques graphically. [ABSTRACT FROM AUTHOR]

In this work, we reformulate and investigate the well-known pantograph differential equation by applying newly-defined conformable operators in both Caputo and Riemann–Liouville settings simultaneously for the first time. In fact, we derive the required existence criteria of solutions corresponding to the inclusion version of the three-point Caputo conformable pantograph BVP subject to Riemann–Liouville conformable integral conditions. To achieve this aim, we establish our main results in some cases including the lower semi-continuous, the upper semi-continuous and the Lipschitz set-valued maps. Eventually, the last part of the present research is devoted to proposing two numerical simulative examples to confirm the consistency of our findings. [ABSTRACT FROM AUTHOR]

Our main purpose in this work is to derive an existence criterion for a Caputo conformable hybrid multi-term integro-differential equation equipped with initial conditions. In this way, we consider a partially ordered Banach space, and, by applying the lower solution property, the existence and successive approximations of solutions for the mentioned hybrid initial problem are investigated. Eventually, we formulate an illustrative example for this hybrid IVP to support our findings from a numerical point of view. Moreover, we plot the sequence of the obtained approximate solutions for different values of noninteger orders. [ABSTRACT FROM AUTHOR]

We study a fractional-order model for the anthrax disease between animals based on the Caputo–Fabrizio derivative. First, we derive an existence criterion of solutions for the proposed fractional CF -system of the anthrax disease model by utilizing the Picard–Lindelof technique. By obtaining the basic reproduction number R 0 of the fractional CF -system we compute two disease-free and endemic equilibrium points and check the asymptotic stability property. Moreover, by applying an iterative approach based on the Sumudu transform we investigate the stability of the fractional CF -system. We obtain approximate series solutions of this system by means of the homotopy analysis transform method, in which we invoke the linear Laplace transform. Finally, after the convergence analysis of the numerical method HATM, we present a numerical simulation of the CF -fractional anthrax disease model and review the dynamical behavior of the solutions of this CF -system during a time interval. [ABSTRACT FROM AUTHOR]

We discuss some existence criteria for a new category of the Caputo conformable differential inclusion furnished with four-point mixed Riemann–Liouville conformable integro-derivative boundary conditions. In this way, we employ some analytical techniques on α-ψ-contractive mappings and operators having the approximate endpoint property to reach desired theoretical results. Finally, we provide an example to illustrate our last main result. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for a new class of fractional q-integro-difference equations involving Riemann-Liouville q-derivatives and a q-integral of different orders, supplemented with boundary conditions containing q-integrals of different orders. The first existence result is obtained by means of Krasnoselskii's fixed point theorem, while the second one relies on a Leray-Schauder nonlinear alternative. The uniqueness result is derived via the Banach contraction mapping principle. Finally, illustrative examples are presented to show the validity of the obtained results. The paper concludes with some interesting observations. [ABSTRACT FROM AUTHOR]

This research is conducted for studying some qualitative specifications of solution to a generalized fractional structure of the standard snap boundary problem. We first rewrite the mathematical model of the extended fractional snap problem by means of the G -operators. After finding its equivalent solution as a form of the integral equation, we establish the existence criterion of this reformulated model with respect to some known fixed point techniques. Then we analyze its stability and further investigate the inclusion version of the problem with the help of some special contractions. We present numerical simulations for solutions of several examples regarding the fractional G -snap system in different structures including the Caputo, Caputo–Hadamard, and Katugampola operators of different orders. [ABSTRACT FROM AUTHOR]