Advances in Difference Equations
Volume 2009 (2009), Article ID 981728, 47 pages
doi:10.1155/2009/981728
A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative
Ravi P. Agarwal1
, Mohammed Belmekki2
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
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.