| Autor: |
Khalid K. Ali, Mohamed S. Mohamed, M. Maneea |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 9, Iss 12, Pp 33442-33466 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.20241596?viewType=HTML |
| Popis: |
This paper presents an innovative approach to solve $ \mathit{q} $-fractional partial differential equations through a combination of two semi-analytical techniques: The Residual Power Series Method (RPSM) and the Homotopy Analysis Method (HAM). Both methods are extended to obtain approximations for $ \mathit{q} $-fractional partial differential equations ($ \mathit{q} $-FPDEs). These equations are significant in $ \mathit{q} $-calculus, which has gained attention due to its relevance in engineering applications, particularly in quantum mechanics. In this study, we solve linear and nonlinear $ \mathit{q} $-FPDEs and obtain the closed-form solutions, which confirm the validity of the utilized methods. The results are further illustrated through two-dimensional and three-dimensional graphs, thus highlighting the interaction between parameters, particularly the fractional parameter, the $ \mathit{q} $-calculus parameter, and time. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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