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