Comparative Analysis of Analytical Solutions for Seepage Flow Derivatives in 4D Porous Media
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i1.5685Keywords:
ADM, FDEs ,FC .Abstract
Accurately modeling seepage flow dynamics in porous media is critical in environmental science, hydrology, and engineering, especially in high-dimensional spaces with fractional derivatives. These flows present significant analytical challenges due to their inherent nonlinearity and complexity. Traditional solution methods often rely on simplifications that reduce accuracy. This study aims to provide a comparative evaluation of three advanced analytical techniques—the Homotopy Analysis Method (HAM), Adomian Decomposition Method (ADM), and Fractional Differential Transform Method (FDTM)—for solving a four-dimensional fractional partial differential equation governing seepage flow. By analyzing the convergence properties, computational efficiency, and solution accuracy of these methods, the study offers insights into their applicability to fractional seepage flow problems in porous media. The findings highlight the strengths and limitations of each approach, guiding researchers in selecting appropriate methods based on the problem’s characteristics and the desired level of accuracy. This comparative analysis advances our understanding of nonlinear fractional systems and their solutions, with implications for envi-
ronmental and engineering applications.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Safa M.Mirgani
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.
By agreeing to this statement, you acknowledge that:
- You retain full copyright over your work.
- The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
- This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.