Table of Contents
ISRN Mathematical Analysis
Volume 2012 (2012), Article ID 868295, 9 pages
http://dx.doi.org/10.5402/2012/868295
Research Article

Existence of Positive Solution to the Cauchy Problem for a Fractional Diffusion Equation with a Singular Nonlinearity

1School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100084, China
2Department of Mathematics, Faculty of Science, China University of Mining and Technology, Beijing 100083, China

Received 16 November 2011; Accepted 17 January 2012

Academic Editor: D. Kouznetsov

Copyright © 2012 Ailing Shi and Shuqin Zhang. 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

Fractional diffusion equations describe an anomalous diffusion on fractals. In this paper, by means of the successive approximation method and other analysis technique, we present a local positive solution to Cauchy problem for a fractional diffusion equation with singular nonlinearity. The fractional derivative is described in the Caputo sense.