A SEMI-ANALYTICAL SOLUTION TO THE TIME-FRACTIONAL ADVECTION–DIFFUSION EQUATION USING FRACTIONAL REDUCED DIFFERENTIAL TRANSFORM METHOD - Akogwu, Blessing O.; Ogunfiditimi, Franklin O. (FUDMA JOURNAL OF SCIENCES, 2025)
A potent tool for simulating models of physical, biological, and dynamic processes is well described by Fractional Partial Differential Equations (FPDE), which is due to their memory effect and non-local properties. The present study applies the Fractional Reduced Differential Transform Method (FRDTM), a semi-analytical technique, to solve Fractional Partial Differential Equations (FPDEs) relevant to advection-diffusion models. The study modifies an existing integer-order model by introducing fractional derivatives and analyzes the influence of these fractional parameters. The FRDTM is validated through comparison with the Fractional Variational Iteration Method (FVIM), thereby demonstrating its accuracy and computational efficiency. Results show that FRDTM performs well in finding an approximate solution for long-time simulations, especially at fractional order α < 1, and is preferable for high accuracy and low computational error, particularly for Advection-Diffusion problems.