Numerical solution of fractional Mathieu equations by using block-pulse wavelets

Abstract

In this paper, we introduce a method based on operational matrix of fractional order integration for the numerical solution of fractional Mathieu equation and then apply it in a number of cases. For this, we use the block-pulse wavelets matrix of fractional order integration with respect to the Caputo sense. The method was tested by some numerical examples and changes occurred in the coefficients as well as in the derivative of the equation. Results prove the accuracy and computational efficiency of the proposed algorithm. Keywords: Block-pulse functions, Fractional calculus, Mathieu differential equation, MSC: 26A33, 93D20, 97N40, 34A08