Advances in Difference Equations
Volume 2009 (2009), Article ID 981728, 47 pages
doi:10.1155/2009/981728
Research Article

A Survey on Semilinear Differential Equations and Inclusions Involving Riemann-Liouville Fractional Derivative

Ravi P. Agarwal,1 Mohammed Belmekki,2 and Mouffak Benchohra2

1Department of Mathematical Sciences, Florida Institute of Technology, Melboune, FL 32901-6975, USA
2Laboratoire de Mathématiques, Université de Sidi Bel Abbès, BP 89, 22000 Sidi Bel Abbès, Algeria

Received 16 July 2008; Revised 4 December 2008; Accepted 5 February 2009

Academic Editor: Alberto Cabada

Copyright © 2009 Ravi P. Agarwal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We establish sufficient conditions for the existence of mild solutions for some densely defined semilinear functional differential equations and inclusions involving the Riemann-Liouville fractional derivative. Our approach is based on the 𝒞0-semigroups theory combined with some suitable fixed point theorems.