A COMPUTATIONAL APPROACH FOR ANALYZING THE APPROXIMATIVE TREATMENT OF FRACTIONAL-ORDERED DIFFUSION PROBLEMS

This study proposes a computational strategy for analyzing the approximative series solutions of time-fractional diffusion problems. We employ the Shehu Homotopy Perturbation Transform Approach (SHPTA), which integrates the Shehu Transform (ST) through the Homotopy Perturbation Approach (HPA). The parameters described within the HPA framework are efficiently managed using He’s polynomials. Fractional-order derivatives are examined within the structure of the Caputo description. Notably, the proposed method operates without any constraints, assumptions, or hypotheses that could distort the fractional problem. To illustrate the effectiveness and applicability of fractional-order derivatives, we provide numerical results through visual representations. The reliability of this approach is evident from the strong agreement between the analytical results and exact solutions. These findings confirm that SHPTA is a robust and efficient technique for representing series solutions to time-fractional problems.