Abstract

In this paper, an operational matrix of integration based on Haar wavelets (HW) is introduced, and a procedure for applying the matrix to solve space and time fractional telegraph equations is formulated. The space and time fractional derivatives are considered in the Caputo sense. The accuracy and effectiveness of the proposed method is demonstrated by the five test problems. Approximate solutions of the space and time fractional telegraph equations are compared with the other numerical solutions and the exact solutions. The proposed scheme can be used in a wide class of linear and nonlinear reaction-diffusion equations. These calculations demonstrate that the accuracy of the Haar wavelet is quite high even in the case of a small number of grid points. The present method is a very reliable, simple, small computation costs, flexible and convenient alternative method. The power of the manageable method is confirmed.

Key words: Haar wavelet, fractional differential equation, decomposition method, telegraph equation, operational matrix of integration.