Advances in Difference Equations
Volume 2011 (2011), Article ID 642013, 15 pages
doi:10.1155/2011/642013
Research Article

Existence Results for a Fractional Equation with State-Dependent Delay

José Paulo Carvalho dos Santos,1 Claudio Cuevas,2 and Bruno de Andrade3

1Instituto de Ciências Exatas, Universidade Federal de Alfenas, 37130-000 Alfenas, MG, Brazil
2Departamento de Matemática, Universidade Federal de Pernambuco, 50540-740 Recife, PE, Brazil
3Departamento de Matemática, ICMC, USP-São Carlos, 13569-970 São Carlos, SP, Brazil

Received 26 August 2010; Revised 14 January 2011; Accepted 7 March 2011

Academic Editor: Dumitru Baleanu

Copyright © 2011 José Paulo Carvalho dos Santos 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 provide sufficient conditions for the existence of mild solutions for a class of abstract fractional integrodifferential equations with state-dependent delay. A concrete application in the theory of heat conduction in materials with memory is also given.