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This paper investigates the existence, uniqueness, and continuous dependence of solutions to fractional order nonlocal thermistor two-point boundary value problems on time scales. We employ the Schauder fixed point theorem to establish the existence of solutions, and the contraction principle to prove uniqueness. We also obtain a result on the continuous dependence of solutions. Finally, we present several examples to illustrate our findings. This work is the first to study a fractional model of thermistor on Department of Medical Research,time scales, and it makes a significant contribution to the field of modeling on time scales. The results of this paper can be used to develop new and improved mathematical models for thermistors, which can be used to design more efficient and reliable thermistor-based devices. [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]

In this study, the dynamics of a novel three-species food chain model featuring the Sokol–Howell functional response are explored. The fear of predators is incorporated into prey reproduction, and refuge is integrated into the middle predators within the framework of the Caputo fractional derivative. Theoretical aspects such as the existence and uniqueness of equilibria, their boundedness, and stability analysis are encompassed in the investigation. To examine the existence of chaos, Lyapunov exponents are computed. The optimal control measure concerning the growth of the prey population was considered, and the conditions that must be met for the optimal response to exist in the optimal control issue were determined using Pontryagin’s Maximum Principle. The theoretical outcomes were validated by using numerical simulation powered by the Adams–Bashforth–Moulton type predictor-corrector technique. Numerical justifications are provided for the influences of fear and refuge factors. When fear is absent, a numerical analysis is conducted on the global stability of the system for fractional order derivative. [ABSTRACT FROM AUTHOR]

The main purpose of the paper is to study the qualitative theory of the solutions of a multi-point sequential Caputo–type p–Laplacian coupled system. The existence and uniqueness of the solution of the aforementioned system are studied with the help of fixed point theorems and properties of a p–Laplacian operator. Furthermore, the Hyers–Ulam stability and generalized Hyers–Ulam stability are also investigated. For the validity of the obtained results, an illustrative example is given. [ABSTRACT FROM AUTHOR]

Due to the importance of some physical systems, in this paper, we aim to investigate a generalized impulsive ρ -Caputo differential equation equipped with a p-Laplacian operator. In fact, our problem is a generalization of fractional differential equations equipped with the integral boundary conditions, impulsive forms and p-Laplacian operators under the Nemytskii operators. In this direction, we prove some theorems on the existence property along with the uniqueness of solutions under the Nemytskii operator. More precisely, we use the Schauder’s and Schaefer’s fixed point theorems, along with the Banach contraction principle. In the sequel, two examples are provided to show the validity of the obtained results in practical. [ABSTRACT FROM AUTHOR]

This inquire about ponder is committed to investigating a few properties in connection to behaviors of solutions to an extended fractional structure of the standard jerk equation. Here, we define the scheme of the general fractional jerk problem using the generalized G operators. The existence result of such a new model is derived and analyzed based on some inequalities and fixed point tools. Furthermore, analysis of its Ulam–Hyers–Rassias type stability is performed and finally, we give numerical simulations for the existing parameters of the mentioned fractional G-jerk system in the Katugampola, Caputo–Hadamard and Caputo settings under different arbitrary orders. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of metric spaces called the Menger probabilistic bipolar metric space and define some other notions related to this space. Moreover, we prove some uniqueness fixed point theorems for two cases including the covariant and contravariant maps. These fixed point theorems are new versions of the Banach contraction principle, Kannan theorem, and Reich-type theorem in the context of the Menger probabilistic bipolar metric space. Throughout the paper, we provide some examples to understand the definitions in the better manner. Finally, two applications are given for proving the uniqueness result in the form of an integral equation and a fractional boundary value problem. [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]

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]

There have been reports of influenza virus resistance in the past, and because this virus has the potential of resistance to cause several pandemics and also is lethal, we investigate the conditions under which the strains coexist as a result. The non-resistant strain undergoes mutation, giving rise to the resistant strain. The incidence rates of the non-resistant and saturated-resistant strains are bi-linear and saturated, respectively. In this study, two flu strain models (resistant and non-resistant) are investigated in a fractal–fractional sense, and the presence of solutions, stability, and numerical simulations are examined for various orders and derivative dimensions. Using numerical values from freely accessible open resources, a numerical technique that is based on Lagrange’s interpolation polynomial is constructed and validated for a particular example. [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 paper establishes a mathematical model of the Zika virus infection with the sexual transmission route under the generalized Caputo-type fractional derivative. The model consists of a system of eleven nonlinear fractional differential equations. The existence and uniqueness results are derived by applying Banach's and Schaüder's fixed point theorems. The different types of Ulam's stability results for the fractional model are examined. The corrector-predictor algorithm has been applied to illustrate the approximated solutions and analyze the dynamical behavior of the fractional model under consideration. In addition, various numerical simulations are presented corresponding to different fractional-orders in α ∈ [ 0 , 1 ] . [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]

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]

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]

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]

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]

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]

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]

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]

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 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 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]

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]

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]

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 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]

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]

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]

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, 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]

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 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]

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]

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]