Global Conference on Mathematics and Applications (GCMA)

This study explores an innovative residual power series method (RPST) for examining time-fractional convection-diffusion equations (TFC-DEqs) that represent transport phenomena with memory and anomalous diffusion characteristics. The methodology is suitable for both linear and nonlinear cases, as it avoids linearization, discretization, and other simplifying assumptions. The reliability of the method is demonstrated by the results, which show strong agreement with exact solutions and rapid convergence as the fractional order approaches one. One of the most significant results of this research is the creation of a dependable and efficient analytical framework that can accommodate intricate transport phenomena without the need for assumptions. The results are significant, as they provide insights and demonstrate promise for potential applications in engineering and applied science, particularly for nonlocal and memory-dependent systems.