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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.