Abstract and Applied Analysis
Volume 2013 (2013), Article ID 784816, 12 pages
http://dx.doi.org/10.1155/2013/784816
Research Article

Nonlocal Problem for Fractional Evolution Equations of Mixed Type with the Measure of Noncompactness

Pengyu Chen and Yongxiang Li

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 8 December 2012; Revised 14 March 2013; Accepted 18 March 2013

Academic Editor: Xinan Hao

Copyright © 2013 Pengyu Chen and Yongxiang Li. 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 general class of semilinear fractional evolution equations of mixed type with nonlocal conditions on infinite dimensional Banach spaces is concerned. Under more general conditions, the existence of mild solutions and positive mild solutions is obtained by utilizing a new estimation technique of the measure of noncompactness and a new fixed point theorem with respect to convex-power condensing operator.