A robust computational algorithm of homotopy asymptotic method for solving systems of fractional differential equations

In this paper, we present new ideas for the implementation of homotopy asymptotic method (HAM) to solve systems of nonlinear fractional differential equations (FDEs). An effective computational algorithm, which is based on Taylor series approximations of the nonlinear equations, is introduced to accelerate the convergence of series solutions. The proposed algorithm suggests a new optimal construction of the homotopy that reduces the computational complexity and improves the performance of the method. Some numerical examples are tested to validate and illustrate the efficiency of the proposed algorithm. The obtained results demonstrate the improvement of the accuracy by the new algorithm.