Numerical Solution of Fractional Differential Equations Using Haar Wavelet Operational Matrix Method

Abstract

In this paper, a new operational matrix method based on Haar wavelets is proposed to solve linear and non-linear differential equations of fractional order. Contrary to wavelet operational methods available in the literature, we derive an explicit form for the Haar wavelet operational matrices of fractional order integration without using the block pulse functions. The main characteristics of our approach is that it converts fractional differential equations to system of algebraic equations and does not require the inverse of the Haar matrices. Illustrative examples are included to demonstrate the validity and applicability of the present method. Moreover, special attention is given to the comparison of the numerical results obtained by the new algorithm with those found by other known methods.