Numerical Solutions of Coupled Fractional Diffusion-Reaction Equations Using q-HMTM and MVIM

Abstract

This paper gives a thorough description of q-Homotopy Mohand Transform Method (q-HMTM) and Mohand Transform Variational Iteration Method in solving nonlinear fractional partial differential equations that characterize an extensive variety of intricate physical and engineering processes. The Caputo-type fractional derivative of these equations provide important memory and hereditary effects. An extensive numerical study is implemented, covering the profiles of the solutions, error tables and two dimensional error plots. Quantitative findings indicate that they both give small absolute errors, with the q-HMTM having a faster convergence and being more stable to measure small variations in the behavior of solutions over different fractional orders. In comparison, Mohand Transform Variational Iteration Method offers accurate approximations at relatively higher error growth with small fractional parameters. The results demonstrate that q-HMTM has high accuracy and computational efficiency, and it is especially applicable when it is needed to simulate systems with nonlocal dynamics.