Hermite collocation method for fractional order differential equations

Abstract

This paper focuses on the approximate solutions of the higher order fractionaldifferential equations with multi terms by the help of Hermite Collocationmethod (HCM). This new method is an adaptation of Taylor’s collocationmethod in terms of truncated Hermite Series. With this method, the differentialequation is transformed into an algebraic equation and the unknowns ofthe equation are the coefficients of the Hermite series solution of the problem.This method appears as an useful tool for solving fractional differential equationswith variable coefficients. To show the pertinent feature of the proposedmethod, we test the accuracy of the method with some illustrative examplesand check the error bounds for numerical calculations.