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

•A class of fractional partial differential equations is solved by HWOM.•The coefficients of the equations are variable in both time and space.•We made an improvement of algorithm to deal such equations.•The error analysis is obtained.

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 equation(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