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Some new existence results and stability concepts for fractional partial random differential equations

Abbas S., Benchohra M., Darwish M. A.

Journal of Mathematics and Applications

2016

Vol. 39

5--22

In the present paper we provide some existence results and Ulam’s type stability concepts for the Darboux problem of partial fractional random differential equations in Banach spaces, by applying the measure of noncompactness and a random fixed point theorem with stochastic domain.

Global existence and stability results for partial fractional random differential equations

Abbas S., Albarakati W., Benchohra M., Hilal E.

Journal of Applied Analysis

2015

Vol. 21, nr 2

79--87

We investigate some existence and stability results for the Darboux problem of partial fractional random differential equations in Banach spaces. Our existence results are based upon some fixed point theorems.

Ulam stabilities for the Darboux problem for partial fractional differential inclusions

Abbas S., Benchohra M.

Demonstratio Mathematica

2014

Vol. 47, nr 4

826--838

In this article, we investigate some Ulam’s type stability concepts for the Darboux problem of partial fractional differential inclusions with a nonconvex valued right hand side. Our results are based upon Covitz-Nadler fixed point theorem and fractional version of Gronwall’s inequality.

Impulsive Hyperbolic System of Partial Differential Equations of Fractional Order with Delay

Benchohra M., Boutefal Z.

Commentationes Mathematicae

2014

Vol 54, No. 2

179--189

This paper deals with the existence of solutions to impulsive partial hyperbolic differential equations with finite delay, involving the Caputo fractional derivative. Our results will be obtained using Krasnoselskii fixed point theorem.

Fractional order Riemann-Liouville integral inclusions with two independent variables and multiple delay

Abbas S., Benchohra M.

Opuscula Mathematica

2013

Vol. 33, no. 2

209--222

In the present paper we investigate the existence of solutions for a system of integral inclusions of fractional order with multiple delay. Our results are obtained upon suitable fixed point theorems, namely the Bohnenblust-Karlin fixed point theorem for the convex case and the Covitz-Nadler for the nonconvex case.

Impulsive partial hyperbolic differential inclusions of fractional order

Abbas S., Benchohra M.

Demonstratio Mathematica

2010

Vol. 43, nr 4

775-797

In this paper we investigate the existence of solutions of a class of partial impulsive hyperbolic differential inclusions involving the Caputo fractional derivative. Our main tools are appropriate fixed point theorems from multivalued analysis.