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Semilinear fractional order integro-differential inclusions with infinite delay

Khalida Aissani, Mouffak Benchohra and Mohamed Abdalla Darwish

Abstract

In this paper, we study the existence of mild solutions for a class of semilinear fractional order integro-differential inclusions with infinite delay in Banach spaces. Sufficient conditions for the existence of solutions are derived by using a nonlinear alternative of Leray–Schauder type for multivalued maps due to Martelli. An example is given to illustrate the theory.

Funding statement: This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, under grant No. (38-130-35-HiCi). The second and third authors, therefore, acknowledge the technical and financial support of KAU.

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Received: 2014-11-19
Accepted: 2015-06-25
Published Online: 2017-01-13
Published in Print: 2018-09-01

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