Wavelets method for the time fractional diffusion-wave equation

In this paper, an efficient and accurate computational method based on the Legendre wavelets (LWs) is proposed for solving the time fractional diffusion-wave equation (FDWE). To this end, a new fractional operational matrix (FOM) of integration for the LWs is derived. The LWs and their FOM of integration are used to transform the problem under consideration into a linear system of algebraic equations, which can be simply solved to achieve the solution of the problem. The proposed method is very convenient for solving such problems, since the initial and boundary conditions are taken into account automatically.