A Legendre-based approach of the optimized decomposition method for solving nonlinear Caputo-type fractional differential equations

In this article, a powerful modification of the optimized decomposition method is presented for dealing with nonlinear fractional differential equations, where the fractional derivatives are described in the Caputo sense. The new modification, the Legendre-based approach of the optimized decomposition method, is suggested by employing the Legendre orthogonal polynomials to construct an optimal decomposition of the series solutions. An illustrative comparison between the Legendre-based approaches of the Adomian decomposition method and the optimized decomposition method is performed to highlight the features and the computational efficiency of the suggested approach. The resulting numerical approximations demonstrate that the approximate solutions of the proposed approach have better accuracy and convergence.