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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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/5602565 |
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| author | Ali Demir Mine Aylin Bayrak Ebru Ozbilge |
| author_facet | Ali Demir Mine Aylin Bayrak Ebru Ozbilge |
| author_sort | Ali Demir |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-56e15e790a134f799b76c6a0b90522ed |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-56e15e790a134f799b76c6a0b90522ed2025-02-03T06:06:41ZengWileyAdvances 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2019/5602565 |
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