التفاصيل البيبلوغرافية
| العنوان: |
Analysis of 2D fractional diffusion equation using the Yang–Abdel–Cattani and Caputo–Fabrizio operators via q-HATM. |
| المؤلفون: |
Alzaid, Sara Salem1 (AUTHOR), Gouri, Aafrin2,3 (AUTHOR) aafringouri30@gmail.com, Alkahtani, Badr Saad T.4 (AUTHOR), Dubey, Ravi Shanker2 (AUTHOR) ravimath13@gmail.com |
| المصدر: |
International Journal of Geometric Methods in Modern Physics. Feb2025, p1. 25p. |
| مستخلص: |
In this paper, we investigate the 2D fractional diffusion equation using the Yang–Abdel–Cattani (YAC) and Caputo–Fabrizio (CF) fractional derivative operators, which offer a novel and efficient framework for addressing fractional calculus problems. We employ the q-Homotopy Analysis Transform Method (q-HATM) to derive the analytical solution to the 2D fractional diffusion equation. A detailed discussion on the existence and uniqueness of the solution is provided, ensuring the robustness of our approach. Furthermore, we present several special cases of the 2D fractional diffusion equation, showcasing the adaptability of the solution method across different scenarios. To validate our results, we perform a comparison with exact solutions, supported by graphical data that highlight the precision of the q-HATM approach. Our study contributes significantly to the growing field of fractional diffusion equations, offering new insights into the applicability of fractional derivative operators. The findings pave the way for future exploration of higher-dimensional diffusion equations and the use of alternative fractional operators in modeling real-world diffusion phenomena across various scientific and engineering domains. [ABSTRACT FROM AUTHOR] |
| قاعدة البيانات: |
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