Abstract and Applied Analysis
Volume 2011 (2011), Article ID 510314, 11 pages
http://dx.doi.org/10.1155/2011/510314
Research Article

Semilinear Volterra Integrodifferential Problems with Fractional Derivatives in the Nonlinearities

Mokhtar Kirane,1 Milan Medveď,2 and Nasser-eddine Tatar3

1Université de la Rochelle, Avenue Michel Crépeau, 17042 La Rochelle Cedex 1, France
2Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Comenius University, Mlynska Doliná, 84248 Bratislava, Slovakia
3Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 29 January 2011; Accepted 7 April 2011

Academic Editor: Allan C. Peterson

Copyright © 2011 Mokhtar Kirane 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

A second-order semilinear Volterra integrodifferential equation involving fractional time derivatives is considered. We prove existence and uniqueness of mild solutions and classical solutions in appropriate spaces.