An Efficient Series Solution for Fractional Differential Equations
We introduce a simple and efficient series solution for a class of nonlinear fractional differential equations of Caputo's type. The new approach is a modified form of the well-known Taylor series expansion where we overcome the difficulty of computing iterated fractional derivatives, which do...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/891837 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549019176402944 |
|---|---|
| author | Mohammed Al-Refai Mohamed Ali Hajji Muhammad I. Syam |
| author_facet | Mohammed Al-Refai Mohamed Ali Hajji Muhammad I. Syam |
| author_sort | Mohammed Al-Refai |
| collection | DOAJ |
| description | We introduce a simple and efficient series solution for a class of nonlinear fractional differential equations of
Caputo's type. The new approach is a modified form of the well-known Taylor series expansion where we overcome the difficulty of computing iterated fractional derivatives, which do not compute in general. The terms of the series are determined sequentially with explicit formula,
where only integer derivatives have to be computed. The efficiency of the new algorithm is illustrated through several examples. Comparison with other series methods such as the Adomian decomposition method and the homotopy perturbation method is made to indicate the efficiency of the new approach. The algorithm can be implemented for a wide class of fractional differential equations with different types of fractional derivatives. |
| format | Article |
| id | doaj-art-39d261e137bb418aa6487e9fcde3d31d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-39d261e137bb418aa6487e9fcde3d31d2025-02-03T06:12:19ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/891837891837An Efficient Series Solution for Fractional Differential EquationsMohammed Al-Refai0Mohamed Ali Hajji1Muhammad I. Syam2Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, UAEDepartment of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, UAEDepartment of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, UAEWe introduce a simple and efficient series solution for a class of nonlinear fractional differential equations of Caputo's type. The new approach is a modified form of the well-known Taylor series expansion where we overcome the difficulty of computing iterated fractional derivatives, which do not compute in general. The terms of the series are determined sequentially with explicit formula, where only integer derivatives have to be computed. The efficiency of the new algorithm is illustrated through several examples. Comparison with other series methods such as the Adomian decomposition method and the homotopy perturbation method is made to indicate the efficiency of the new approach. The algorithm can be implemented for a wide class of fractional differential equations with different types of fractional derivatives.http://dx.doi.org/10.1155/2014/891837 |
| spellingShingle | Mohammed Al-Refai Mohamed Ali Hajji Muhammad I. Syam An Efficient Series Solution for Fractional Differential Equations Abstract and Applied Analysis |
| title | An Efficient Series Solution for Fractional Differential Equations |
| title_full | An Efficient Series Solution for Fractional Differential Equations |
| title_fullStr | An Efficient Series Solution for Fractional Differential Equations |
| title_full_unstemmed | An Efficient Series Solution for Fractional Differential Equations |
| title_short | An Efficient Series Solution for Fractional Differential Equations |
| title_sort | efficient series solution for fractional differential equations |
| url | http://dx.doi.org/10.1155/2014/891837 |
| work_keys_str_mv | AT mohammedalrefai anefficientseriessolutionforfractionaldifferentialequations AT mohamedalihajji anefficientseriessolutionforfractionaldifferentialequations AT muhammadisyam anefficientseriessolutionforfractionaldifferentialequations AT mohammedalrefai efficientseriessolutionforfractionaldifferentialequations AT mohamedalihajji efficientseriessolutionforfractionaldifferentialequations AT muhammadisyam efficientseriessolutionforfractionaldifferentialequations |