Hermite collocation method for fractional order differential equations

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