Pade Method for Construction of Numerical Algorithms for Fractional Initial Value Problem

الملخص EN

In this paper, we propose an efficient method for constructing numerical algorithms for solving the fractional initial value problem by using the Pade approximation of fractional derivative operators.

We regard the Grunwald–Letnikov fractional derivative as a kind of Taylor series and get the approximation equation of the Taylor series by Pade approximation.

Based on the approximation equation, we construct the corresponding numerical algorithms for the fractional initial value problem.

Finally, we use some examples to illustrate the applicability and efficiency of the proposed technique.