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Semilinear fractional order integro-differential equations with infinite delay in Banach spaces

Khalida Aissani; Mouffak Benchohra — 2013

Archivum Mathematicum

This paper concerns the existence of mild solutions for fractional order integro-differential equations with infinite delay. Our analysis is based on the technique of Kuratowski’s measure of noncompactness and Mönch’s fixed point theorem. An example to illustrate the applications of main results is given.

Fractional integro-differential inclusions with state-dependent delay

Khalida Aissani; Mouffak Benchohra; Khalil Ezzinbi — 2014

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we establish sufficient conditions for the existence of mild solutions for fractional integro-differential inclusions with state-dependent delay. The techniques rely on fractional calculus, multivalued mapping on a bounded set and Bohnenblust-Karlin's fixed point theorem. Finally, we present an example to illustrate the theory.

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