Time-Space Fractional Heat Equation in the Unit Disk

Time-Space Fractional Heat Equation in the Unit Disk

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...

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Main Authors: Rabha W. Ibrahim, Hamid A. Jalab
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/364042
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spelling doaj-d710d56c115a468aaec0b70c673db1362020-11-24T23:38:12ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/364042364042Time-Space Fractional Heat Equation in the Unit DiskRabha W. Ibrahim0Hamid A. Jalab1Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, MalaysiaFaculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, MalaysiaWe 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.http://dx.doi.org/10.1155/2013/364042
collection DOAJ
language English
format Article
sources DOAJ
author Rabha W. Ibrahim
Hamid A. Jalab
spellingShingle Rabha W. Ibrahim
Hamid A. Jalab
Time-Space Fractional Heat Equation in the Unit Disk
Abstract and Applied Analysis
author_facet Rabha W. Ibrahim
Hamid A. Jalab
author_sort Rabha W. Ibrahim
title Time-Space Fractional Heat Equation in the Unit Disk
title_short Time-Space Fractional Heat Equation in the Unit Disk
title_full Time-Space Fractional Heat Equation in the Unit Disk
title_fullStr Time-Space Fractional Heat Equation in the Unit Disk
title_full_unstemmed Time-Space Fractional Heat Equation in the Unit Disk
title_sort time-space fractional heat equation in the unit disk
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description 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.
url http://dx.doi.org/10.1155/2013/364042
work_keys_str_mv AT rabhawibrahim timespacefractionalheatequationintheunitdisk
AT hamidajalab timespacefractionalheatequationintheunitdisk
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