Towards Efficient Solutions of Space-Time Fractional Fuzzy Diffusion Equations: A Methodological Approach

Mousavi Nasr, Mohammad; Asgari, Mohammad  Sadegh; Ziamanesh, Mohsen

doi:10.22111/ijfs.2024.48473.8544

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, P.O. Box 13185/768, Tehran, Iran.

https://doi.org/10.22111/ijfs.2024.48473.8544

Abstract

This paper aims to introduce a groundbreaking methodology for deriving analytical solutions to the space-time fractional fuzzy diffusion equation. Our approach uniquely incorporates a Caputo generalized Hukuhara fractional derivative (of order $\beta \in (0,2]$) for the second-order spatial derivative, alongside a fuzzy Caputo-Katugampola generalized Hukuhara time-fractional derivative (of order $\alpha \in (0,1)$) for the first-order temporal derivative. The primary objective is to develop explicit and fundamental solutions for both the space-time fractional fuzzy diffusion equation and the time fractional fuzzy diffusion equation, encompassing various forms of fuzzy Caputo-Katugampola generalized Hukuhara time-fractional differentiability. We initiate our study by thoroughly analyzing the fuzzy Fourier and fuzzy $\wp-$Laplace transforms of the equation. To demonstrate the practical utility and effectiveness of our proposed method, we apply it to two specific models: a fuzzy groundwater flow model for computing pressure head, and a fuzzy model for determining the concentration of tumor cells. The results obtained highlight the method's efficiency and precision in addressing the complexities of both the space-time fractional fuzzy diffusion equation and the time fractional fuzzy diffusion equation.

Keywords

Main Subjects

Fuzzy Math

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Towards Efficient Solutions of Space-Time Fractional Fuzzy Diffusion Equations: A Methodological Approach

References

References

Volume 21, Issue 4July and August 2024Pages 179-195

Volume 21, Issue 4
July and August 2024
Pages 179-195