Power Series Method for Linear Partial Differential Equations of Fractional Order

Abstract

In this article, a novel numerical method is proposed for linear partial differential equations with time-fractional derivatives. This method is based on power series and generalized Taylor's formula. The fractional derivatives are considered in the Caputo sense. Several illustrative examples are given to demonstrate the effectiveness of the present method. The modified algorithm provides approximate solutions in the form of convergent series with easily computable components. The obtained results are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, efficient and easy to implement.