Mouffak Benchohra

• PhD
• Research Director at Université Djillali Liabes de Sidi-Bel-Abbes

This paper deals with some existence results for a class of conformable implicit fractional differential Hybrid equations with delay. The results are based on some suitable fixed point theorems. In the last section, we provide different examples to illustrate our obtained results.

In this paper, we present some results concerning the existence and Ulam stabilities of random solutions for some functional integral equations of Hadamard fractional order and random effects in Fréchet spaces. We provide an example to illustrate our obtained results.

This article deals with the existence and stability results for a class of implicit fractional differential equations involving the Caputo tempered fractional derivative with retarded and advanced arguments. The results are based on Sadovskii's fixed point theorem. Some examples are given to show the applicability of our results.

In this article, we study the existence of PC-asymptotically almost automorphic mild solutions of integro-differential equations with nonlocal conditions via resolvent operators in Banach space. Further, we give sufficient conditions for the solutions to depend continuously on the initial condition. Finally, an example is given to validate the theo...

In this paper, we present some results on existence, uniqueness and Ulam stability for a class of problems for nonlinear implicit random fractional differential equations with Caputo tempered fractional derivative. For our proofs, we employ some suitable fixed point theorems. Finally, we provide some illustrative examples.

This article focuses on investigating the existence of solutions for a specific category of fractional differential inclusions with non-instantaneous impulses. These inclusions involve the Hilfer fractional derivative in Banach space. The outcomes derived from our research are established through the utilization of Darbo and Monch's fixed point the...

The aim of this paper is to present existence, Ulam-Hyers-Rassias stability and continuous dependence on initial conditions for the mild solution of impulsive integro-differential systems via resolvent operators. Our analysis is based on fixed point theorem with generalized measures of noncompactness, this approach is combined with the technique th...

This paper deals with the existence and uniqueness of periodic solutions for a nonlinear fractional pantograph coupled system with ψ-Caputo derivative. We employ the coincidence degree theory of Mawhin to established our proofs. An illustration will be presented to demonstrate the validity of the given result.

This paper deals with some existence results for a class of conformable implicit fractional differential equations with instantaneous impulses infinite delay. The results are based on Schaefer's fixed point theorem. We illustrate our results by an example in the last section.

The main goal of this paper is to study the existence and uniqueness of periodic solutions for a problem with fractional differential equation involving the Caputo tempered fractional derivative. The proofs are based upon the coincidence degree theory of Mawhin. To show the efficiency of the stated result, two illustrative examples will be demonstr...

The focus of this paper is the investigation of a particular type of nonlinear deformable fractional differential equations, and analyzing their existence results. Our approach involves utilizing relevant fixed point theorems, we also explore the global convergence of successive approximations to provide additional insights into the topic. To furth...

This paper addresses matters pertaining to the existence of solutions, both oscillatory and nonoscillatory, for specific class of Caputo tempered fractional differential equations and inclusions. We achieve this through the application of set-valued analysis, Schauder's and Martelli's fixed point theorems, and the approach involving upper and lower...

This article is a subject about some results of the existence and Ulam stability results for four classes of implicit neutral fractional differential equations involving the Caputo tempered fractional derivative with delay. The results are based on Krasnoselskii's fixed point theorem in Banach spaces, and the notion of the stability of Ulam kind. T...

This article deals with the existence of solutions to a boundary value problem for the Caputo type modification of the Erdélyi-Kober fractional differential equations. Our primary results are demonstrated by combining the fixed point theorems of Darbo and Mönch with the approach of measures of noncompactness. Furthermore, an example is provided to...

The main objective of this paper is to investigate several aspects including the existence, uniqueness, and κ-Mittag-Leffler-Ulam-Hyers stability of a specific class of terminal value problems. These problems involve implicit nonlinear fractional differential equations and tempered (κ, ψ)-Hilfer fractional derivatives. To accomplish this, we employ...

The focus of this paper is on investigating a particular type of nonlinear (λ, ψ)-Hilfer fractional differential equations, and analyzing their existence results. Our approach involves utilizing Banach's fixed point theorem, and we also explore the global convergence of successive approximations to provide additional insights into the topic. To fur...

The purpose of this article is to study the existence, uniqueness and Ulam stability results for a class of implicit neutral fractional di¤erential equations involving the Caputo tempered fractional derivative with retarded and advanced arguments. The results are based on Banach's contraction principle, Schauder's and Darbo's …xed point theorems. T...

In this article, we discuss the existence of extremal solutions for a class of nonlinear sequential δ-Caputo fractional differential equations involving nonlinear boundary conditions. Our results are founded on advanced functional analysis methods. To be more specific, we use the monotone iterative approach in conjunction with the upper and lower s...

In this paper, we present some results on the existence and uniqueness of the class of problems for nonlinear fractional differential equations with some new generalized conformable derivatives with retardation and anticipation. For our proofs, we employ some suitable fixed-point theorems. Finally, we provide two illustrative examples.

This paper deals with some existence of solutions for some classes of coupled systems of conformable fractional differential equations with initial and boundary conditions in Banach and Fréchet spaces. Our results are based on some fixed point theorems. Some illustrative examples are presented in the last section.

This paper delves into the investigation of existence and uniqueness results concerning the Hilfer–Katugampola random nonlinear fractional differential coupled system within a generalized Banach space. Such problems represent a broadened scope, extending several existing results in the literature and offering potential avenues for furthering the de...

In this paper, we present findings concerning the existence of solutions to a particular type of nonlocal second-order delay semilinear integro-differential equation with time-varying evolution. We utilize the theory of the resolvent family, the Kuratowski measure of noncompactness, and fixed point theorems in conjunction with a convex-power conden...

In this article, we study the existence of mild solutions of a non-instantaneous integrodifferential equations on unbounded domain via resolvent operators in Banach space. For our proofs, we employ the semigroups theory and Schauder's fixed point theorem. Moreover, we show that solutions of our problem are attractive. Finally, an example is given t...

This manuscript is devoted to proving some results concerning the existence of solutions for a class of initial value problem for nonlinear implicit fractional Hybrid differential equations and improved conformable fractional derivative. The result is based on a fixed point theorem due to Dhage. Further, an example is provided for the justification...

This paper discusses the existence of solution for integro-differential equations via resolvent operators in Banach space. Our approach is based on a new fixed point theorem with respect to Meir-Keeler condensing operators. An example is given to show the application of our result.

The main goal of this article is to study the existence and uniqueness of periodic solutions for the implicit problem with nonlinear fractional differential equation involving the Caputo tempered fractional derivative. The proofs are based upon the coincidence degree theory of Mawhin. To show the efficiency of the stated result, two illustrative ex...

In this work, we investigate the existence of mild solutions and controllability of integrodifferential equations subject to a state-dependent nonlocal condition on an unbounded interval in the α-norm, all under the assumption of noncom-pactness of the resolvent operator. To address this problem, we apply fractional power operators and a generaliza...

In this paper, we generalize the ψ-Hilfer fractional derivative and discuss some of its properties. We prove existence, uniqueness and stability results for a class of initial value problems for implicit nonlinear fractional differential equations involving generalized ψ-Hilfer fractional derivative. The uniqueness result for the given problem is o...

In this paper, we investigates the existence of periodic mild solutions for a class of impulsive Integro-differential inclusions. We base our arguments on fixed point theory paired with the approach of measure of noncompactness using the resolvent operator. Finally, an illustration of our results is presented.

This paper explores the existence and stability of implicit neutral Caputo fractional q-difference equations within four distinct classes, incorporating various delay types such as finite, infinite, and state-dependent delays. To establish the existence of solutions, we utilize the fixed point theorem of Krasnoselskii in Banach spaces. The concludi...

The main goal of this paper is to study the existence and uniqueness of periodic solutions for some class of nonlinear fractional coupled systems with ψ−Hilfer derivative. The proofs are based upon the coincidence degree theory of Mawhin with several types of conditions. To show the efficiency of the stated result, illustrative examples will be giv...

This paper is devoted to the existence of random mild solutions for a general class of second-order abstract random differential equations with state-dependent delay. The technique used is a generalization of the classical Darbo fixed point theorem for Fréchet spaces associated with the concept of measures of noncompactness. An application related...

In this paper, we study the existence of solutions for hybrid fractional differential equations with p-Laplacian operator involving fractional Caputo derivative of arbitrary order. This work can be seen as an extension of earlier research conducted on hybrid differential equations. Notably, the extension encompasses both the fractional aspect and t...

In this paper, we shall establish sufcient conditions for the existence, approximate controllability, and Ulam-Hyers-Rassias stability of solutions for impulsive integrodiferential equations of second order with state-dependent delay using the resolvent operator theory, the approximating technique, Picard operators, and the theory of fxed point wit...

In this article, we present some results on existence, uniqueness, and Ulam-Hyers-Rassias stability for a class of nonlinear improved conformable fractional differential equations with Retardation and Anticipation. Our reasoning is based on some relevant fixed point theorems .

The primary focus of this paper is threefold: first, to investigate the existence of mild solutions; second, to analyze the topological and geometrical structure of the solution sets; and third, to determine the continuous dependence of the solution for second-order semilinear integro-differential inclusion. In this study, we employ Bohnenblust-Kar...

This paper deals with some existence and uniqueness results for a class of deformable fractional differential equations. These problems encompassed nonlinear implicit fractional differential equations involving boundary conditions and various types of delays, including finite, infinite, and state-dependent delays. Our approach to proving the existe...

This paper discusses the global convergence of successive approximations methods for solving integro-differential equation via resolvent operators in Banach spaces. We prove a theorem on the global convergence of successive approximations to the unique solution of the problems. An example is given to show the application of our result.

Fractional Difference, Differential Equations, and Inclusions: Analysis and Stability is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for several classes of functional fractional difference equations and inclusions. Covered equations include delay effects of finite, infinite, or state-d...

The primary focus of this study is to explore the presence of a mild solution within a specific category of fractional non-autonomous differential evolution equations, incorporating integral impulse conditions. The approach employed extends the classical Darbo fixed point theorem for Fréchet spaces, leveraging the notion of a measure of noncompactn...

In this paper, we investigate the existence of asymptoti-cally almost automorphic mild solution for a class of integro-differential equations. The existence results are established through the application of Mönch's fixed point theorem and the utilization of measures of non-compactness. Additionally, we present an illustrative example to showcase t...

Our research is primarily focused on applying the tempered (κ, ψ)-fractional operators to investigate the existence, uniqueness, and κ-Mittag-Leffler-Ulam-Hyers stability of a specific class of boundary value problems involving implicit nonlinear fractional differential equations and tempered (κ, ψ)-Hilfer fractional derivatives. To accomplish this...

This article is a subject about the existence results for a class of tempered ψ-Caputo fractional differential equations. These problems encompassed nonlinear implicit neutral fractional differential equations involving various types of delays, including finite, infinite, and state-dependent delays. The results are based on the concept of the degre...

This article deals with some existence and uniqueness results for several classes of implicit fractional differential equations with delay. Our results are based on some fixed point theorems. To illustrate our results, we present some examples in the last section. Mathematics Subject Classification (2010): 26A33, 34A08, 34K37.

In this paper, we investigate the existence and Ulam stability results for a class of boundary value problems for implicit Riesz-Caputo fractional differential equations with non-instantaneous impulses involving both retarded and advanced arguments. The result are based on Mönch fixed point theorem associated with the technique of measure of noncom...

This paper deals with the existence and uniqueness results for a class of impulsive implicit fractional initial value problems of the convex combined Caputo fractional derivative. The arguments are based on Banach's contraction principle, Schauder's and Mönch's fixed point theorems. We will also establish the Ulam stability and give some examples t...

The purpose of this article is to study the existence and Ulam-Hyers stability results for a class of boundary value problems with Caputo tempered fractional derivative and infinite delay. The results are based on Mönch's fixed point theorem. An illustrative example is given to demonstrate the applicability of our results.

This paper is concerned with some existence and uniqueness results for a class of problems for nonlinear Caputo tempered implicit fractional differential equations in b-Metric spaces with three-point boundary conditions. The results are based on the −-Geraghty type contraction, the-contraction and the fixed point theory. In addition, two illustrati...

This paper deals with some existence results for a class of Caputo-Katugampola implicit impulsive fractional differential equations with infinite delay. The results are based on the Schaefer's fixed point theorem. We illustrate our results by an example in the last section.

Fractional calculus is a branch of mathematics which deals with the derivatives and integrals of arbitrary (noninteger) order. Though the subject is as old as conventional calculus, the applications are rather recent. The researchers Grunwald, Letnikov, L’Hopital, Leibniz, Hardy, Caputo, Mainardi, and others did pioneering work in this field. The k...

This paper deals with some existence results for a class of conformable implicit fractional differential equations with delay in b-metric spaces. The results are based on the α − φ-Geraghty type contraction and the fixed point theory. We illustrate our results by an example in the last section.

This paper deals with some existence and uniqueness results for a class of problems for nonlinear Caputo tempered implicit fractional differential equations in b-Metric spaces with initial nonlocal conditions and instantaneous impulses. The results are based on the −-Geraghty type contraction, the F-contraction and the fixed point theory. Furthermo...

This paper deals with some existence and uniqueness results for a class of problems for nonlinear Caputo tempered implicit fractional differential equations in b-Metric spaces with initial nonlocal conditions and instantaneous impulses. The results are based on the ω − δ-Geraghty type contraction, the F-contraction and the fixed point theory. Furth...

This paper introduces novel definitions of the tempered (k, ψ)-fractional operators and establishes their various properties. Our research focuses on applying these new findings to investigate the existence and uniqueness of solutions for a specific class of initial value problems concerning implicit nonlinear fractional differential equations and...

In this work, we propose sufficient conditions guaranteeing an existence result of mild solutions by using the nonlinear Leray-Schauder alternative in Banach spaces combined with the semigroup theory for the class of Caputo partial semilinear fractional evolution equations with finite state-dependent delay and nonlocal conditions. Proyecciones Jou...

The objective of this paper is to introduce new definitions of the tempered (κ, ψ)-fractional operators and establish their various properties. Our research is primarily focused on applying these newly proposed operators to investigate the existence, uniqueness, and κ-Mittag-Leffler-Ulam-Hyers stability of a specific class of boundary value problem...

The present paper deals with some existence results for the Dar-boux problem of partial fractional random differential equations with finite delay. The arguments are based on a random fixed point theorem with stochastic domain combined with the measure of noncompactness. An illustration is given to show the applicability of our results.

This paper is concerned with some existence and uniqueness results for a class of problems for nonlinear Caputo tempered implicit fractional differential equations in b-Metric spaces with three-point boundary conditions. The results are based on the ω −-Geraghty type contraction, the-contraction and the fixed point theory. In addition, two illustra...

This research delves into the field of fractional differential equations with both non-instantaneous impulses and delay within the framework of Banach spaces. Our objective is to establish adequate conditions that ensure the existence, uniqueness, and Ulam-Hyers-Rassias stability results for our problems. The studied problems encompass abstract imp...

In this paper, we investigate existence of mild solutions to a non-instantaneous integrodifferential equation via resolvent operators in the sense of Grimmer in Fréchet spaces. Utilizing the technique of measures of noncompactness in conjunction with the Darbo's fixed point theorem, we present sufficient criteria ensuring the controllability of the...

In this paper, we study the existence of mild solution for impulsive fractional differential inclusions in Banach spaces involving the Hilfer derivative. Our study is based on the non-linear alternative of Leray-Schauder type for multivalued maps due to Martelli. An example will be added to illustrate the main result.

This study examines if there are any mild solutions for the perturbed partial functional and neutral functional evolution equations with state-dependent delay when the derivative utilizes Caputo’s fractional derivative, as well as whether any such solutions are unique. The solution itself determines how long the equations take to solve. The work pr...

The main goal of this paper is to study the existence and uniqueness of periodic solutions for some class of nonlinear fractional pantograph systems with Ψ-Hilfer derivative. The proofs are based upon the coincidence degree theory of Mawhin. To show the efficiency of the stated result, an illustrative example will be demonstrated.

This chapter is devoted to proving some results concerning the existence of solutions for a class of initial and boundary value problems for nonlinear fractional Hybrid differential equations and Generalized Hilfer fractional derivative.

In this chapter, we prove some existence and uniqueness results for a class of boundary and terminal value problems for implicit nonlinear k-generalized \(\psi \)-Hilfer fractional differential equations involving both retarded and advanced arguments. Further, examples are given to illustrate the viability of our results in each section.

This chapter deals with some existence and uniqueness results for a class of coupled systems for nonlinear k-generalized \(\psi \)-Hilfer fractional differential equations with boundary and terminal conditions. Our results are based on some necessary fixed point theorems. Furthermore, an illustration is presented for each section to demonstrate the...

This chapter deals with the existence and uniqueness results for a class of impulsive initial and boundary value problems for implicit nonlinear fractional differential equations and k-Generalized \(\psi \)-Hilfer fractional derivative involving both retarded and advanced arguments. Our results are based on some necessary fixed point theorems. Suit...

This chapter discusses the mathematical tools, notations, and concepts that will be required in subsequent chapters.

This article deals with the existence, uniqueness and Ulam-Hyers-Rassias stability results for a class of coupled systems for implicit fractional differential equations with Riesz-Caputo fractional derivative and boundary conditions. We will employ the Banach's contraction principle as well as Schauder's fixed point theorem to demonstrate our exist...

In this paper, we demonstrate various existence and uniqueness results for a class of deformable implicit fractional differential equations with delay in b-metric spaces with boundary conditions. We base our arguments on some suitable fixed point theorems. In the last section, we provide different examples to illustrate our obtained results.

This paper deals with some existence results for a class of k-generalised ψ-Hilfer implicit fractional differential equations in b-metric spaces. The results are based on the α − ϕ-Geraghty type contraction and the fixed point theory. We illustrate our results by an example in the last section.

In this paper, we study the existence of integral solutions of a functional differential equation with delay and random effects. We base our arguments on some suitable random fixed point theorem with stochastic domain and the integrated semigroup.

The purpose of this study is to use resolvent operators to investigate the existence and the controllability of a mild solution to a second-order semilinear integro-differential problem. To construct our criterion, we use a fixed point theorem in conjunction with measures of noncompactness. A practical example is used to illustrate the obtained res...

This manuscript is devoted to proving some results concerning the existence of solutions for a class of initial value problems for nonlinear fractional Hybrid differential equations and Generalized Hilfer fractional derivative. The result is based on a fixed point theorem due to Dhage. Further , some examples are provided for the justification of o...

In this article, we present some results on the existence and uniqueness of random solutions to a non-linear implicit fractional differential equation involving the generalized Caputo fractional derivative operator and supplemented with non-local and periodic boundary conditions. We make use of the fixed point theorems due to Banach and Krasnoselsk...

This chapter deals with some existence results for a class of coupled systems for implicit nonlinear k-generalized ψ-Hilfer fractional differential equations with terminal conditions. The tools employed for this study are the fixed point theorem of Mönch combined with the technique of measure of noncompactness. Furthermore, an example is provided t...

This chapter deals with some existence and Ulam stability results for a class of initial and boundary value problems for differential equations with generalized Hilfer-type fractional derivative in Banach spaces.

The aim of this chapter is to prove some existence, uniqueness, and Ulam-Hyers-Rassias stability results for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and generalized Hilfer-type fractional derivative. We base our arguments on some relevant fixed point theorems combined with the techniq...

The present chapter deals with some existence, uniqueness, and Ulam stability results for a class of initial and boundary value problems for nonlinear implicit fractional differential equations with non-instantaneous impulses and generalized Hilfer-type fractional derivative. The tools employed are some suitable fixed point theorems combined with t...

In this chapter, we discuss the necessary mathematical tools, notations, and concepts we need in the succeeding chapters. We look at some essential properties of fractional differential operators. We also review some of the basic properties of measures of noncompactness and fixed point theorems which are crucial in our results regarding fractional...

In this paper, we study the following fractional differential equation involving the Atangana-Baleanu-Caputo fractional derivative: { A B C a D τ θ [ x ( ϑ ) − F ( ϑ , x ( ϑ ) ) ] = G ( ϑ , x ( ϑ ) ) , ϑ ∈ J : = [ a , b ] , x ( a ) = φ a ∈ ℝ . $$\left\{ {\matrix{ {AB{C_a}D_\tau ^\theta [x(\vartheta ) - F(\vartheta ,x(\vartheta ))] = G(\vartheta ,x(...

The aim of this paper is to study the existence of the unique mild solution for non-linear fractional integro-differential equations with state-dependent nonlocal condition. The result was obtained by using nonlinear alternative of Granas-Frigon for contraction in Fréchet spaces. To illustrate the result, an example is provided.

This paper aims to explore the existence results of a certain type of Caputo fractional q-difference equations in Banach spaces. To achieve this goal, we employ a fixed point theorem that relies on the concept of measure of noncompactness and the convex-power condensing operator. We give an illustrative example in the last section.

This paper deals with some existence and uniqueness results for a class of problems for nonlinear Caputo tempered implicit fractional differential equations in b-Metric spaces with initial condition and infinite delay. The results are based on the ω−ψ-Geraghty type contraction, the F-contraction and the fixed point theory. Furthermore, an two illus...

In this paper, we investigate the existence and Ulam-Hyers-Rassias stability results for a class of functional integrodifferential evolution equations with state-dependent delay and non-instantaneous impulsions on infinite intervals via resolvent operators in the sense of Grimmer. Our analysis is based on fixed point theorem with measures of noncom...