A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations
A hybrid analytical method for solving linear and nonlinear fractional partial differential equations is presented. The proposed analytical approach is an elegant combination of the Natural Transform Method (NTM) and a well-known method, Homotopy Perturbation Method (HPM). In this analytical method,...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2016/9207869 |
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| _version_ | 1832562598753599488 |
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| author | Shehu Maitama |
| author_facet | Shehu Maitama |
| author_sort | Shehu Maitama |
| collection | DOAJ |
| description | A hybrid analytical method for solving linear and nonlinear fractional partial differential equations is presented. The proposed analytical approach is an elegant combination of the Natural Transform Method (NTM) and a well-known method, Homotopy Perturbation Method (HPM). In this analytical method, the fractional derivative is computed in Caputo sense and the nonlinear term is calculated using He’s polynomial. The proposed analytical method reduces the computational size and avoids round-off errors. Exact solution of linear and nonlinear fractional partial differential equations is successfully obtained using the analytical method. |
| format | Article |
| id | doaj-art-4d666bdfb07749028dad9efc673125c6 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-4d666bdfb07749028dad9efc673125c62025-02-03T01:22:10ZengWileyInternational Journal of Differential Equations1687-96431687-96512016-01-01201610.1155/2016/92078699207869A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential EquationsShehu Maitama0Department of Mathematics, Faculty of Science, Northwest University, Kano, NigeriaA hybrid analytical method for solving linear and nonlinear fractional partial differential equations is presented. The proposed analytical approach is an elegant combination of the Natural Transform Method (NTM) and a well-known method, Homotopy Perturbation Method (HPM). In this analytical method, the fractional derivative is computed in Caputo sense and the nonlinear term is calculated using He’s polynomial. The proposed analytical method reduces the computational size and avoids round-off errors. Exact solution of linear and nonlinear fractional partial differential equations is successfully obtained using the analytical method.http://dx.doi.org/10.1155/2016/9207869 |
| spellingShingle | Shehu Maitama A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations International Journal of Differential Equations |
| title | A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations |
| title_full | A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations |
| title_fullStr | A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations |
| title_full_unstemmed | A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations |
| title_short | A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations |
| title_sort | hybrid natural transform homotopy perturbation method for solving fractional partial differential equations |
| url | http://dx.doi.org/10.1155/2016/9207869 |
| work_keys_str_mv | AT shehumaitama ahybridnaturaltransformhomotopyperturbationmethodforsolvingfractionalpartialdifferentialequations AT shehumaitama hybridnaturaltransformhomotopyperturbationmethodforsolvingfractionalpartialdifferentialequations |