A matrix expansion solution for a hyperbolic system of time-fractional PDEs with variable coefficients

In this research, we introduce a series solution to a hyperbolic system of time-fractional partial differential equations with variable coefficients in the sense of Caputo fractional derivative. An appropriate expansion of matrix functions is derived and used to create a series solution for the target problem and the residual power series method is also used to determine the coefficients of the series solution. To test our proposed method, we discuss four interesting and important applications. The first three applications are set up so that the exact solution is already known whereas the last application is set up without knowing the solution in advance to test the predictability of the solution or obtain a suitable approximate solution. Numerical results are analyzed to confirm the ability of the used method and to verify the solution obtained. The surface graphs of the solution are plotted to illustrate the behavior of the solution in various conditions. Mathematica 7 software is used to calculate the numerical and symbolic quantities.