Showing papers by "Mouffak Benchohra published in 2023"
2 citations
TL;DR: In this paper , the issue of approximate controllability for a certain class of abstract neutral integro-differential equations having non-instantaneous impulsions and being subject to state-dependent delay is investigated.
Abstract: In this manuscript, we investigate the issue of approximate controllability for a certain class of abstract neutral integro-differential equations having non-instantaneous impulsions and being subject to state-dependent delay. Our methodology relies on the utilization of resolvent operators in conjunction with Darbo’s fixed point theorem. To exemplify the practical implications of our findings, we provide an illustration.
01 Jan 2023
TL;DR: In this paper , the authors explore fractional differential equations with a fixed point approach, based on many years of research, and present a fixed-point approach to solve the problem.
Abstract: This book explores fractional differential equations with a fixed point approach, based on many years of research.
TL;DR: In this article , the existence and uniqueness results for a class of problems systems for nonlinear k $$ k $$ -generalized ψ $$ \psi $$ -Hilfer fractional differential equations with periodic conditions are discussed.
Abstract: This paper deals with some existence and uniqueness results for a class of problems systems for nonlinear k $$ k $$ -generalized ψ $$ \psi $$ -Hilfer fractional differential equations with periodic conditions. The arguments are based on Mawhin's coincidence degree theory. Furthermore, an illustration is presented to demonstrate the plausibility of our results.
TL;DR: In this paper , the existence and global stability of solutions of a new class of Volterra partial integral equations of Hadamard-Stieltjes in the fractional order were investigated.
Abstract: This paper deals with the existence and global stability of solutions of a
new class of Volterra partial integral equations of Hadamard-Stieltjes
fractional order.
TL;DR: In this article , 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 were obtained.
Abstract: Abstract 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 existence results. We provide an example to illustrate the obtained results.
TL;DR: In this article , the existence and uniqueness results for a class of problems for nonlinear Caputo tempered implicit fractional differential equations in b-metric spaces with initial and nonlocal conditions are discussed.
Abstract: Abstract This paper deals with the existence and uniqueness results for a class of problems for nonlinear Caputo tempered implicit fractional differential equations in b-metric spaces with initial and nonlocal conditions. The arguments are based on some fixed point theorems. Furthermore, two illustrations are presented to demonstrate the plausibility of our results.
TL;DR: In this paper , the existence of the unique mild solution for non-linear fractional integro-differential equations with state-dependent nonlocal condition was studied. And the result was obtained by using nonlinear alternative of Granas-Frigon for contraction in Fréchet spaces.
Abstract: Abstract 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.
TL;DR: In this paper , a result of existence and uniqueness of solutions for the following class of problems of initial value for differential equations with maxima and Caputo's fractional order on the time scales was proved.
Abstract: In this paper, we prove a result of existence and uniqueness of solutions for
the following class of problem of initial value for differential equations
with maxima and Caputo?s fractional order on the time scales: c??a u(?) =
?(?, u(?), max ??[a,?] u(?)), ? ? J := [a, b]T, 0 < ? ? 1, u(a) = ?, We used
the techniques of the Picard and weakly Picard operators to obtain some data
dependency on the parameters results.
TL;DR: In this article , the Atangana-Baleanu-Caputo fractional derivative was studied and the result is based on a fixed point theorem, and an example is provided for the justification of the main result.
Abstract: Abstract In this paper, we study the following fractional differential equation involving the Atangana-Baleanu-Caputo fractional derivative: { ABCaDτθ[x(ϑ)−F(ϑ,x(ϑ))]=G(ϑ,x(ϑ)), ϑ∈J:=[a,b],x(a)=φa∈ℝ. $$\left\{ {\matrix{ {AB{C_a}D_\tau ^\theta [x(\vartheta ) - F(\vartheta ,x(\vartheta ))] = G(\vartheta ,x(\vartheta )),\;\;\;{\kern 1pt} \vartheta \in J: = [a,b],} \hfill \cr {x(a) = {\varphi _a} \in .} \hfill \cr } } \right.$$ The result is based on a Dhage fixed point theorem. Further, an example is provided for the justification of our main result.
TL;DR: In this paper , the existence results for a class of k-generalized ψ-Hilfer implicit fractional differential equations in b-metric spaces were derived based on the α-φ-Geraghty type contraction and fixed point theory.
Abstract: This paper deals with some existence results for a class of k-generalized 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.
TL;DR: In this article , the authors used resolvent operators to investigate the existence and controllability of a mild solution to a second-order semilinear integro-differential problem.
Abstract: 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 results.