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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 364042, 7 pages
http://dx.doi.org/10.1155/2013/364042
Time-Space Fractional Heat Equation in the Unit Disk
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.