Higher order methods for fractional differential equation based on fractional backward differentiation formula of order three

摘要

In this paper, a family of explicit methods are presented based on the fractional backward differentiation formula of order three for the numerical solution of the fractional differential equations. The major part of the paper is focused on the study of the stability properties of the introduced methods. The intervals of stability for multistep methods have been calculated and a number of numerical examples are given to confirm theoretical results.