Modified Fractional Power Series Method for solving fractional partial differential equations
The literature revealed that the Fractional Power Series Method (FPSM), which uses the Mittag-Leffler function in one parameter, has been gainfully applied in obtaining the solutions of fractional partial differential equations (FPDEs) in one dimension. However, the solutions in the multi-dimensiona...
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| Language: | English |
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Elsevier
2024-12-01
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| Series: | Scientific African |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2468227624004095 |
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| author | Isaac Addai Benedict Barnes Isaac Kwame Dontwi Kwaku Forkuoh Darkwah |
| author_facet | Isaac Addai Benedict Barnes Isaac Kwame Dontwi Kwaku Forkuoh Darkwah |
| author_sort | Isaac Addai |
| collection | DOAJ |
| description | The literature revealed that the Fractional Power Series Method (FPSM), which uses the Mittag-Leffler function in one parameter, has been gainfully applied in obtaining the solutions of fractional partial differential equations (FPDEs) in one dimension. However, the solutions in the multi-dimensional space have not been explored by researchers across the globe. The solutions of the FPDEs are feasible with the involvement of parameter α in the Mittag-Leffler function. However, the FPSM, which uses the Mittag-Leffler function in two parameters, has not been considered by researchers. Incorporating two parameters, α and β, in the Mittag-Leffler function of the FPSM is beyond reasonable doubt; it provides the continuum solution of the FPDEs and also yields more consistent and fast convergence of the solution in Holder’s spaces compared to the FPSM with the Mittag-Leffler function in one parameter. The FPSM is extended by replacing the Mittag-Leffler function in one parameter with the Mittag-Leffler function in two parameters. Also, the modified FPSM is applied to obtain the solutions of both heat and telegraph equations in multi-dimensions and one-dimension respectively. The solutions obtained by the FPSM with the Mittag-Leffler function in one parameter are compared with the modified FPSM using the Mittag-Leffler function in two parameters. |
| format | Article |
| id | doaj-art-61042f1f4e6d4236a47a20439292e2cc |
| institution | OA Journals |
| issn | 2468-2276 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Scientific African |
| spelling | doaj-art-61042f1f4e6d4236a47a20439292e2cc2025-08-20T02:32:22ZengElsevierScientific African2468-22762024-12-0126e0246710.1016/j.sciaf.2024.e02467Modified Fractional Power Series Method for solving fractional partial differential equationsIsaac Addai0Benedict Barnes1Isaac Kwame Dontwi2Kwaku Forkuoh Darkwah3Corresponding author.; Kwame Nkrumah University of Science and Technology, Mathematics Department, GhanaKwame Nkrumah University of Science and Technology, Mathematics Department, GhanaKwame Nkrumah University of Science and Technology, Mathematics Department, GhanaKwame Nkrumah University of Science and Technology, Mathematics Department, GhanaThe literature revealed that the Fractional Power Series Method (FPSM), which uses the Mittag-Leffler function in one parameter, has been gainfully applied in obtaining the solutions of fractional partial differential equations (FPDEs) in one dimension. However, the solutions in the multi-dimensional space have not been explored by researchers across the globe. The solutions of the FPDEs are feasible with the involvement of parameter α in the Mittag-Leffler function. However, the FPSM, which uses the Mittag-Leffler function in two parameters, has not been considered by researchers. Incorporating two parameters, α and β, in the Mittag-Leffler function of the FPSM is beyond reasonable doubt; it provides the continuum solution of the FPDEs and also yields more consistent and fast convergence of the solution in Holder’s spaces compared to the FPSM with the Mittag-Leffler function in one parameter. The FPSM is extended by replacing the Mittag-Leffler function in one parameter with the Mittag-Leffler function in two parameters. Also, the modified FPSM is applied to obtain the solutions of both heat and telegraph equations in multi-dimensions and one-dimension respectively. The solutions obtained by the FPSM with the Mittag-Leffler function in one parameter are compared with the modified FPSM using the Mittag-Leffler function in two parameters.http://www.sciencedirect.com/science/article/pii/S2468227624004095FSPM with Mittag-Leffler function in two parametersFSPM with Mittag-Leffler function in one parameterConvergence of solution |
| spellingShingle | Isaac Addai Benedict Barnes Isaac Kwame Dontwi Kwaku Forkuoh Darkwah Modified Fractional Power Series Method for solving fractional partial differential equations Scientific African FSPM with Mittag-Leffler function in two parameters FSPM with Mittag-Leffler function in one parameter Convergence of solution |
| title | Modified Fractional Power Series Method for solving fractional partial differential equations |
| title_full | Modified Fractional Power Series Method for solving fractional partial differential equations |
| title_fullStr | Modified Fractional Power Series Method for solving fractional partial differential equations |
| title_full_unstemmed | Modified Fractional Power Series Method for solving fractional partial differential equations |
| title_short | Modified Fractional Power Series Method for solving fractional partial differential equations |
| title_sort | modified fractional power series method for solving fractional partial differential equations |
| topic | FSPM with Mittag-Leffler function in two parameters FSPM with Mittag-Leffler function in one parameter Convergence of solution |
| url | http://www.sciencedirect.com/science/article/pii/S2468227624004095 |
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