Abstract

In this study, we utilized the Kamal residual power series method to solve the fractional-order population diffusion equation in the Caputo sense. This method combines the residual power series method with the Kamal transformation integral. The procedure starts by defining the approximate solution of a power series with unknown coefficients; the residual function is then constructed. By imposing the condition, the coefficients can be easily calculated, and finally, the approximate series solution is found. Three different figures were used to evaluate the strategy’s accuracy and effectiveness. This method offers a significant advantage: it negates the requirement for computing Adomian polynomials, considering perturbation processes, or performing linearization.