Exploring fractional Advection-Dispersion equations with computational methods: Caputo operator and Mohand techniques

This study presented a comprehensive analysis of nonlinear fractional systems governed by the advection-dispersion equations (ADE), utilizing the Mohand transform iterative method (MTIM) and the Mohand residual power series method (MRPSM). By incorporating the Caputo fractional derivative, we enhanced the modeling capability for fractional-order differential equations, accounting for nonlocal effects and memory in the systems dynamics. We demonstrated that both MTIM and validated against exact results. The steady-state solutions, complemented by graphical representations, highlighted the behavior of the system for varying fractional orders and showcased the flexibility and robustness of the methods. These findings contributed significantly to the field of computational physics, offering powerful tools for tackling complex fractional-order systems and advancing research in related fields.