On the Inverse Problem of the Fractional Heat-Like Partial Differential Equations: Determination of the Source Function

On the Inverse Problem of the Fractional Heat-Like Partial Differential Equations: Determination of the Source Function

The study in this paper mainly concerns the inverse problem of determining an unknown source function in the linear fractional differential equation with variable coefficient using Adomian decomposition method (ADM). We apply ADM to determine the continuous right hand side functions fx and ft in the...

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Main Authors: Gülcan Özkum, Ali Demir, Sertaç Erman, Esra Korkmaz, Berrak Özgür
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2013/476154
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spelling doaj-6d4f4a910df342209fbf2dfa4fc094fc2021-07-02T13:54:26ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392013-01-01201310.1155/2013/476154476154On the Inverse Problem of the Fractional Heat-Like Partial Differential Equations: Determination of the Source FunctionGülcan Özkum0Ali Demir1Sertaç Erman2Esra Korkmaz3Berrak Özgür4Department of Mathematics, Science and Letter Faculty, Kocaeli University, Umuttepe Campus, 41380 Kocaeli, TurkeyDepartment of Mathematics, Science and Letter Faculty, Kocaeli University, Umuttepe Campus, 41380 Kocaeli, TurkeyDepartment of Mathematics, Science and Letter Faculty, Kocaeli University, Umuttepe Campus, 41380 Kocaeli, TurkeyArdahan University, 75000 Ardahan, TurkeyDepartment of Mathematics, Science and Letter Faculty, Kocaeli University, Umuttepe Campus, 41380 Kocaeli, TurkeyThe study in this paper mainly concerns the inverse problem of determining an unknown source function in the linear fractional differential equation with variable coefficient using Adomian decomposition method (ADM). We apply ADM to determine the continuous right hand side functions fx and ft in the heat-like diffusion equations Dtαux,t=hxuxxx,t+fx and Dtαux,t=hxuxxx,t+ft, respectively. The results reveal that ADM is very effective and simple for the inverse problem of determining the source function.http://dx.doi.org/10.1155/2013/476154
collection DOAJ
language English
format Article
sources DOAJ
author Gülcan Özkum
Ali Demir
Sertaç Erman
Esra Korkmaz
Berrak Özgür
spellingShingle Gülcan Özkum
Ali Demir
Sertaç Erman
Esra Korkmaz
Berrak Özgür
On the Inverse Problem of the Fractional Heat-Like Partial Differential Equations: Determination of the Source Function
Advances in Mathematical Physics
author_facet Gülcan Özkum
Ali Demir
Sertaç Erman
Esra Korkmaz
Berrak Özgür
author_sort Gülcan Özkum
title On the Inverse Problem of the Fractional Heat-Like Partial Differential Equations: Determination of the Source Function
title_short On the Inverse Problem of the Fractional Heat-Like Partial Differential Equations: Determination of the Source Function
title_full On the Inverse Problem of the Fractional Heat-Like Partial Differential Equations: Determination of the Source Function
title_fullStr On the Inverse Problem of the Fractional Heat-Like Partial Differential Equations: Determination of the Source Function
title_full_unstemmed On the Inverse Problem of the Fractional Heat-Like Partial Differential Equations: Determination of the Source Function
title_sort on the inverse problem of the fractional heat-like partial differential equations: determination of the source function
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2013-01-01
description The study in this paper mainly concerns the inverse problem of determining an unknown source function in the linear fractional differential equation with variable coefficient using Adomian decomposition method (ADM). We apply ADM to determine the continuous right hand side functions fx and ft in the heat-like diffusion equations Dtαux,t=hxuxxx,t+fx and Dtαux,t=hxuxxx,t+ft, respectively. The results reveal that ADM is very effective and simple for the inverse problem of determining the source function.
url http://dx.doi.org/10.1155/2013/476154
work_keys_str_mv AT gulcanozkum ontheinverseproblemofthefractionalheatlikepartialdifferentialequationsdeterminationofthesourcefunction
AT alidemir ontheinverseproblemofthefractionalheatlikepartialdifferentialequationsdeterminationofthesourcefunction
AT sertacerman ontheinverseproblemofthefractionalheatlikepartialdifferentialequationsdeterminationofthesourcefunction
AT esrakorkmaz ontheinverseproblemofthefractionalheatlikepartialdifferentialequationsdeterminationofthesourcefunction
AT berrakozgur ontheinverseproblemofthefractionalheatlikepartialdifferentialequationsdeterminationofthesourcefunction
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