Abstract and Applied Analysis
Volume 2012 (2012), Article ID 131652, 41 pages
http://dx.doi.org/10.1155/2012/131652
Research Article

On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces

Marko Kostić,1 Cheng-Gang Li,2 and Miao Li2

1Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia
2Department of Mathematics, Sichuan University, Chengdu 610064, China

Received 18 June 2012; Revised 5 August 2012; Accepted 5 August 2012

Academic Editor: Dumitru Băleanu

Copyright © 2012 Marko Kostić 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

This paper is devoted to the study of abstract time-fractional equations of the following form: , , , , where , and are closed linear operators on a sequentially complete locally convex space , , is an -valued function, and denotes the Caputo fractional derivative of order (Bazhlekova (2001)). We introduce and systematically analyze various classes of -regularized ( )-existence and uniqueness (propagation) families, continuing in such a way the researches raised in (de Laubenfels (1999, 1991), Kostić (Preprint), and Xiao and Liang (2003, 2002). The obtained results are illustrated with several examples.