Numerical method to initial-boundary value problems for fractional partial differential equations with time-space variable coefficients

Abstract

In this paper, Haar wavelet operational matrix(HWOM) is proposed to solve initial-boundary value problems for a class of time-space fractional partial differential equations of Caputo sense with variable coefficients in both time and space(1)∑i=1nθi∂γiu(x,t)∂tγi=v(x,t)∂αu(x,t)∂xα+d(x,t)∂βu(x,t)∂xβ+q(x,t),0<x<1,0<t≤1,as an extension of Rehman and Khan's (2013) work. We obtain a matrix L instead of Qα in Rehman and Khan (2013). when dealing with boundary conditions. By utilizing the operational matrix of fractional integration and Hadamard product,we made an improvement of algorithm to deal with time-space coefficients and gave the error analysis of the HWOM for space-time dimensions. Some numerical results are paralleled with exact solutions to show the efficiency and precision of the presented technique.