Haar Wavelet Operational Matrix Method for the Numerical Solution of Fractional Order Differential Equations

[摘要] In this paper, we propose a new operational matrix method of fractional order integration based on Haar wavelets to solve fractional order differential equations numerically. The properties of Haar wavelets are first presented. The properties of Haar wavelets are used to reduce the system of fractional order differential equations to a systemof algebraic equationswhich can be solved numerically byNewton’s method.Moreover, the proposed method is derived without using the block pulse functions considered in open literature and does not require the inverse of the Haar matrices. Numerical examples are included to demonstrate the validity and applicability of the present method.

[关键词] Haar wavelet;Homotopy analysis transform method;Fractional order differential equations;Haar matrix;Operational matrix;Error analysis