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...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2024-12-01
|
| Series: | Scientific African |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2468227624004095 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 2468-2276 |