A reliable modification of the rectangular decomposition method

In this paper, we present a powerful modification of the rectangular decomposition method that is used to solve fractional diffusion-wave equations. The new modification extends the application of the rectangular decomposition method to solve a wide class of space-time fractional partial differential equations. The proposed modification gives an analytical solution in the form of a convergent series with easily computable components. Some numerical examples are given to illustrate the efficiency and reliability of the method. The new modification introduces a promising tool for many partial differential equations.