A New Approach for the Approximate Analytical Solution of Space-Time Fractional Differential Equations by the Homotopy Analysis Method

A New Approach for the Approximate Analytical Solution of Space-Time Fractional Differential Equations by the Homotopy Analysis Method

The motivation of this study is to construct the truncated solution of space-time fractional differential equations by the homotopy analysis method (HAM). The first space-time fractional differential equation is transformed into a space fractional differential equation or a time fractional different...

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Main Authors: Ali Demir, Mine Aylin Bayrak, Ebru Ozbilge
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2019/5602565
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spelling doaj-56e15e790a134f799b76c6a0b90522ed2021-07-02T07:35:09ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/56025655602565A New Approach for the Approximate Analytical Solution of Space-Time Fractional Differential Equations by the Homotopy Analysis MethodAli Demir0Mine Aylin Bayrak1Ebru Ozbilge2Department of Mathematics, University of Kocaeli, Kocaeli, TurkeyDepartment of Mathematics, University of Kocaeli, Kocaeli, TurkeyAmerican University of the Middle East, Department of Mathematics and Statistics, Egaila, KuwaitThe motivation of this study is to construct the truncated solution of space-time fractional differential equations by the homotopy analysis method (HAM). The first space-time fractional differential equation is transformed into a space fractional differential equation or a time fractional differential equation before the HAM. Then the power series solution is constructed by the HAM. Finally, taking the illustrative examples into consideration we reach the conclusion that the HAM is applicable and powerful technique to construct the solution of space-time fractional differential equations.http://dx.doi.org/10.1155/2019/5602565
collection DOAJ
language English
format Article
sources DOAJ
author Ali Demir
Mine Aylin Bayrak
Ebru Ozbilge
spellingShingle Ali Demir
Mine Aylin Bayrak
Ebru Ozbilge
A New Approach for the Approximate Analytical Solution of Space-Time Fractional Differential Equations by the Homotopy Analysis Method
Advances in Mathematical Physics
author_facet Ali Demir
Mine Aylin Bayrak
Ebru Ozbilge
author_sort Ali Demir
title A New Approach for the Approximate Analytical Solution of Space-Time Fractional Differential Equations by the Homotopy Analysis Method
title_short A New Approach for the Approximate Analytical Solution of Space-Time Fractional Differential Equations by the Homotopy Analysis Method
title_full A New Approach for the Approximate Analytical Solution of Space-Time Fractional Differential Equations by the Homotopy Analysis Method
title_fullStr A New Approach for the Approximate Analytical Solution of Space-Time Fractional Differential Equations by the Homotopy Analysis Method
title_full_unstemmed A New Approach for the Approximate Analytical Solution of Space-Time Fractional Differential Equations by the Homotopy Analysis Method
title_sort new approach for the approximate analytical solution of space-time fractional differential equations by the homotopy analysis method
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2019-01-01
description The motivation of this study is to construct the truncated solution of space-time fractional differential equations by the homotopy analysis method (HAM). The first space-time fractional differential equation is transformed into a space fractional differential equation or a time fractional differential equation before the HAM. Then the power series solution is constructed by the HAM. Finally, taking the illustrative examples into consideration we reach the conclusion that the HAM is applicable and powerful technique to construct the solution of space-time fractional differential equations.
url http://dx.doi.org/10.1155/2019/5602565
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AT ebruozbilge anewapproachfortheapproximateanalyticalsolutionofspacetimefractionaldifferentialequationsbythehomotopyanalysismethod
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