Convergence analysis of the fractional decomposition method with applications to time‐fractional biological population models

Abstract In this study, we present convergence analysis along with an error estimate for time‐fractional biological population equation in terms of the Caputo derivative using a new technique called the fractional decomposition method (FDM). Further, we present exact solutions to four test problems of nonlinear time‐fractional biological population models to show the accuracy and efficiency of the FDM. This method based on constructing series solutions in a form of rapidly convergent series with easily computable components and without the need of linearization, discretization and perturbations. The results prove that the FDM is very effective and simple for solving fractional partial differential equations in multi‐dimensional spaces, special cases of which we have described in this paper.