Abstract and Applied Analysis
Volume 2013 (2013), Article ID 364042, 7 pages
http://dx.doi.org/10.1155/2013/364042
Research Article

Time-Space Fractional Heat Equation in the Unit Disk

Rabha W. Ibrahim1 and Hamid A. Jalab2

1Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia
2Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia

Received 2 December 2012; Accepted 12 February 2013

Academic Editor: Juan J. Trujillo

Copyright © 2013 Rabha W. Ibrahim and Hamid A. Jalab. 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 will study a maximal solution of the time-space fractional heat equation in complex domain. The fractional time is taken in the sense of the Riemann-Liouville operator, while the fractional space is assumed in the Srivastava-Owa operator. Here we employ some properties of the univalent functions in the unit disk to determine the upper bound of this solution. The maximal solution is illustrated in terms of the generalized hypergeometric functions.