Advances in Difference Equations
Volume 2011 (2011), Article ID 584874, 13 pages
doi:10.1155/2011/584874
Research Article

Weighted 𝑆 -Asymptotically 𝜔 -Periodic Solutions of a Class of Fractional Differential Equations

Claudio Cuevas,1 Michelle Pierri,2 and Alex Sepulveda3

1Departamento de Matemática, Universidade Federal de Pernambuco, 50540-740 Recife, PE, Brazil
2Departamento de Física e Matemática da Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, 14040-901 Ribeirão Preto, SP, Brazil
3Departamento de Matemática y Estadística, Universidad de La Frontera, Casilla 54-D, Temuco, Chile

Received 23 September 2010; Accepted 8 December 2010

Academic Editor: J. J. Trujillo

Copyright © 2011 Claudio Cuevas 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 study the existence of weighted 𝑆 -asymptotically 𝜔 -periodic mild solutions for a class of abstract fractional differential equations of the form 𝑢 = 𝜕 − 𝛼 + 1 A u + 𝑓 ( 𝑡 , 𝑢 ) , 1 < 𝛼 < 2 , where 𝐴 is a linear sectorial operator of negative type.