Numerical Solution of Fractional Partial Differential Equation of Parabolic Type Using Chebyshev Wavelets Method

Numerical solution of the fractional differential equation is almost an important topic in recent years. In this paper, in order to solve the numerical solution of a class of fractional partial differential equation of parabolic type, we present a collocation method of two-dimensional Chebyshev wavelets. Using the definition and property of Chebyshev wavelets, we give the definition of two-dimensional Chebyshev wavelets. We transform the initial problems into solving a system of nonlinear algebraic equations by applying the wavelets collocation method. Convergence analysis is investigated to show that the method is convergent. The numerical example shows the effectiveness of the approach.