Numerical Analysis for the Variable Order Time Fractional Diffusion-Wave Equation

Time fractional order partial derivative equations are the generalization of the traditional integer order partial derivative equations, in which the time fractional order derivative is used to replace the corresponding integer order derivative. In this paper, the variable order time fractional diffusion-wave equation is considered. Firstly, numerical approximation scheme has been proposed by using the method of the piecewise linear interpolation join with a second order approximation of the first order time derivative to discrete the Coimbra variable order time fractional derivative. Then, central difference is used to approximate the second order of the spatial fractional derivatives. Finally, a numerical example has been presented to verify the numerical technique, which shows the efficiency of the numerical method.