Year: 2025
Type: article
Abstract: This article develops a finite element method (FEM) for solving nonlinear fractional-order partial differential equations (PDEs) using the Caputo fractional derivative. The scheme achieves second-order convergence in L2 and L∞ norms and is supported by a rigorous qualitative analysis, including existence, uniqueness, and Ulam-Hyers stability, established via nonlinear functional analysis and fixed-point theorems. Applied to a fractionalorder Burgers' equation modeling longitudinal dispersion in homogeneous porous media, the method demonstrates superior accuracy compared to finite difference and B-spline Galerkin methods. Numerical results validate robustness across fractional orders α ∈ {0.5, 0.75, 1.0}, with applications in environmental engineering and fluid dynamics.
DOI: 10.11948/20250026
Authors: Tejas Sharma, Shreekant Pathak, Gargi Trivedi, Vishant Shah, Bhavyata Patel, Trupti Shah
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7088539426