Search results for: Mouffak Benchohra

Items from 1 to 20 out of 74 results

article

On implicit fractional q‐difference equations: Analysis and stability

Nadjet Laledj, Abdelkrim Salim, Jamal Eddine Lazreg, Saïd Abbas, more

Mathematical Methods in the Applied Sciences > 45 > 17 > 10775 - 10797

This paper deals with some existence and Ulam stability results for some classes of implicit fractional

q

‐difference equations with and without random effects in Banach spaces and Banach algebras. Our results are provided by applying the fixed point theory (Itoh's random fixed point theorem, the nonlinear alternative of Schaefer's type proved by Dhage, and an other Dhage's random fixed point...

article

Extremal solutions to a coupled system of nonlinear fractional differential equations with ψ–Caputo fractional derivatives

Choukri Derbazi, Zidane Baitiche, Mouffak Benchohra, John R. Graef

Journal of Mathematics and Applications > 2021 > Vol. 44 > 19--34

Using the well-known monotone iterative technique together with the method of upper and lower solutions, the authors investigate the existence of extremal solutions to a class of coupled systems of nonlinear fractional differential equations involving the ψ–Caputo derivative with initial conditions. As applications of this work, two illustrative examples are presented.

article

Existence and Ulam stability for implicit fractional q-difference equations

Saïd Abbas, Mouffak Benchohra, Nadjet Laledj, Yong Zhou

Advances in Difference Equations > 2019 > 2019 > 1 > 1-12

This paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section.

article

Fractional hybrid differential equations with three-point boundary hybrid conditions

Choukri Derbazi, Hadda Hammouche, Mouffak Benchohra, Yong Zhou

Advances in Difference Equations > 2019 > 2019 > 1 > 1-11

In this paper, we study the existence of solutions for hybrid fractional differential equations involving fractional Caputo derivative of order 1<α≤2 $1 < \alpha\leq 2$. Our results rely on a hybrid fixed point theorem for a sum of three operators due to Dhage. An example is provided to illustrate the theory.

article

Oscillation and nonoscillation for Caputo–Hadamard impulsive fractional differential inclusions

Mouffak Benchohra, Samira Hamani, Yong Zhou

Advances in Difference Equations > 2019 > 2019 > 1 > 1-15

In this paper, the concept of upper and lower solutions method combined with the fixed point theorem is used to investigate the existence of oscillatory and nonoscillatory solutions for a class of initial value problem for Caputo–Hadamard impulsive fractional differential inclusions.

article

Semilinear fractional differential equations with infinite delay and non-instantaneous impulses

Mouffak Benchohra, Sara Litimein, Juan J. Nieto

Journal of Fixed Point Theory and Applications > 2019 > 21 > 1 > 1-16

In this article, we study the existence of mild solutions for a new class of impulsive semilinear fractional differential equations with infinite delay and non-instantaneous impulses in Banach spaces. The new results are obtained using suitable fixed point theorems and the technique of measures of noncompactness. An example is also given to illustrate the obtained theory.

article

Caputo–Hadamard fractional differential Cauchy problem in Fréchet spaces

Saïd Abbas, Mouffak Benchohra, Farida Berhoun, Johnny Henderson

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales.... > 2019 > 113 > 3 > 2335-2344

This article deals with some existence results of solutions for a class of differential equations involving the Caputo–Hadamard fractional derivative in Fréchet spaces. These results are based on a generalization of the classical Darbo fixed point theorem for Fréchet spaces associated with the concept of measure of noncompactness. We illustrate our results by an example.

article

Existence and Ulam stability for nonlinear implicit differential equations with Riemann-Liouville fractional derivative

Mouffak Benchohra, Soufyane Bouriah, Juan J. Nieto

Demonstratio Mathematica > 2019 > Vol. 52, nr 1 > 437--450

In this paper, we establish the existence and uniqueness of solutions for a class of initial value problem for nonlinear implicit fractional differential equations with Riemann-Liouville fractional derivative, also, the stability of this class of problem. The arguments are based upon the Banach contraction principle and Schaefer’s fixed point theorem. An example is included to show the applicability...

article

Coupled Hilfer fractional differential systems with random effects

Saïd Abbas, Mouffak Benchohra, Yong Zhou

Advances in Difference Equations > 2018 > 2018 > 1 > 1-12

This paper deals with some existence results for two classes of coupled systems of Hilfer and Hilfer–Hadamard random fractional differential equations. The main tool used to carry out our results is Itoh’s random fixed point theorem.

article

Implicit coupled Hilfer–Hadamard fractional differential systems under weak topologies

Saïd Abbas, Mouffak Benchohra, Naima Hamidi, Yong Zhou

Advances in Difference Equations > 2018 > 2018 > 1 > 1-17

In this article, we present some existence of weak solutions for a coupled system of implicit fractional differential equations of Hilfer–Hadamard type. Our approach is based on Mönch’s fixed point theorem associated with the technique of measure of weak noncompactness.

article

Weak solutions for a coupled system of Pettis-Hadamard fractional differential equations

Saïda Abbas, Mouffak Benchohra, Yong Zhou, Ahmed Alsaedi

Advances in Difference Equations > 2017 > 2017 > 1 > 1-11

In this paper, by applying the technique of measure of weak noncompactness and Mönch’s fixed point theorem, we investigate the existence of weak solutions under the Pettis integrability assumption for a coupled system of Hadamard fractional differential equations.

article

Boundary Value Problems for Nonlinear Implicit Caputo–Hadamard-Type Fractional Differential Equations with Impulses

Mouffak Benchohra, Soufyane Bouriah, John R. Graef

Mediterranean Journal of Mathematics > 2017 > 14 > 5 > 1-21

In this paper, the authors establish the existence and uniqueness of solutions for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and Caputo–Hadamard type fractional derivatives. The stability of this problem is also studied. The arguments are based on the Banach contraction principle and Schaefer’s fixed point theorem. Two examples are presented...

article

A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability

Saïd Abbas, Mouffak Benchohra, Jamal-Eddine Lazreg, Yong Zhou

Chaos, Solitons & Fractals > 2017 > 102 > C > 47-71

In the present survey paper, we prove some results concerning the existence of solutions and weak solutions for some classes of Hadamard and Hilfer fractional differential equations. Some attractivity and Ulam stability results are presented. Our results are provided by applying the fixed point theory, and the technique of strong and weak measures of noncompactness.

article

Stability results for partial fractional differential equations with noninstantaneous impulses

Saïd Abbas, Mouffak Benchohra, Ahmed Alsaedi, Yong Zhou

Advances in Difference Equations > 2017 > 2017 > 1 > 1-22

In this article, we investigate some uniqueness and Ulam’s type stability concepts for the Darboux problem of partial functional differential equations with noninstantaneous impulses and delay in Banach spaces. The main techniques rely on fractional calculus, integral equations and inequalities. Two examples are also provided to illustrate our results.

article

Existence of periodic solutions for nonlinear implicit Hadamard’s fractional differential equations

Mouffak Benchohra, Soufyane Bouriah, Juan J. Nieto

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales.... > 2018 > 112 > 1 > 25-35

In this paper, by applying the coincidence degree theory which was first introduced by Mawhin, we obtain an existence result for a class of problem for nonlinear implicit fractional differential equations (IFDE for short) with Hadamard fractional derivative. We present two examples to show the applicability of our results.

article

Measure of Noncompactness and Partial Functional Differential Equations with State-Dependent Delay

Mouffak Benchohra, Imene Medjadj

Differential Equations and Dynamical Systems > 2018 > 26 > 1-3 > 139-155

Our aim in this work is to study the existence of solutions of first and second order functional differential equations with state-dependent delay. We use the Mönch’s fixed point theorem for the existence of solutions and the concept of measures of noncompactness.

article

Global existence and stability for functional evolution equations with state-dependent delay

Eman Alaidarous, Wafaa Albarakati, Abdessalam Baliki, Mouffak Benchohra

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales.... > 2017 > 111 > 1 > 15-24

In this paper we prove some results on the global existence and attractivity of mild solutions for semilinear evolution equations with state-dependent delay in Banach space.

article

Existence and attractivity for the Darboux problem of fractional order neutral differential equations

Saïd Abbas, Mouffak Benchohra, Johnny Henderson, Boualem Attou Slimani

Journal of Applied Mathematics and Computing > 2016 > 52 > 1-2 > 73-85

In this paper, we prove an existence result and we initiate the question of attractivity of solutions for initial value problems (IVP for short), for fractional order neutral differential equations with finite delay. The proof of the main result is based on Krasnosel’skii’s fixed point theorem.

article

Global Existence Results for Neutral Functional Differential Equations with State-Dependent Delay

Mouffak Benchohra, Imene Medjadj

Differential Equations and Dynamical Systems > 2016 > 24 > 2 > 189-200

Our aim in this work is to study the existence of solutions of a neutral functional differential equation with state-dependent delay. We use the Schauder’s fixed point theorem to show the existence of global solutions.

article

Ulam stabilities for partial Hadamard fractional integral equations

Saïd Abbas, Wafaa Albarakati, Mouffak Benchohra, Juan J. Trujillo

Arabian Journal of Mathematics > 2016 > 5 > 1 > 1-7

This paper deals with some existence and Ulam stability results for a class of partial integral equations via Hadamard’s fractional integral, by applying Schauder’s fixed-point theorem.

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INFONA - science communication portal

Search results for: Mouffak Benchohra

On implicit fractional q‐difference equations: Analysis and stability

Extremal solutions to a coupled system of nonlinear fractional differential equations with ψ–Caputo fractional derivatives

Existence and Ulam stability for implicit fractional q-difference equations

Fractional hybrid differential equations with three-point boundary hybrid conditions

Oscillation and nonoscillation for Caputo–Hadamard impulsive fractional differential inclusions

Semilinear fractional differential equations with infinite delay and non-instantaneous impulses

Caputo–Hadamard fractional differential Cauchy problem in Fréchet spaces

Existence and Ulam stability for nonlinear implicit differential equations with Riemann-Liouville fractional derivative

Coupled Hilfer fractional differential systems with random effects

Implicit coupled Hilfer–Hadamard fractional differential systems under weak topologies

Weak solutions for a coupled system of Pettis-Hadamard fractional differential equations

Boundary Value Problems for Nonlinear Implicit Caputo–Hadamard-Type Fractional Differential Equations with Impulses

A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability

Stability results for partial fractional differential equations with noninstantaneous impulses

Existence of periodic solutions for nonlinear implicit Hadamard’s fractional differential equations

Measure of Noncompactness and Partial Functional Differential Equations with State-Dependent Delay

Global existence and stability for functional evolution equations with state-dependent delay

Existence and attractivity for the Darboux problem of fractional order neutral differential equations

Global Existence Results for Neutral Functional Differential Equations with State-Dependent Delay

Ulam stabilities for partial Hadamard fractional integral equations

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