Efficient Solution of Fractional Initial Value Problems Using Expanding Perturbation Approach

In this article, expanding perturbation approach is applied for solving the initial value problems with fractional coordinate derivatives. The fractional derivative is described in the Caputo sense. The response expressions are written in terms of the Mittag-Leffler functions. Convergence of the approach is proved. Comparisons are made to confirm the reliability and effectiveness of the present ideas.