A Vector Series Solution for a Class of Hyperbolic System of Caputo Time-Fractional Partial Differential Equations With Variable Coefficients

In this paper, we introduce a series solution to class of hyperbolic system time-fractional partial differential equations with variable coefficients. The fractional derivative has been considered by the concept Caputo. Two expansions matrix functions are proposed and used create solutions for target problem. first one is Laurent series, second power series. A new approach, via residual method Laplace transform, also find coefficients solution. order test our method, discuss four interesting important applications. Numerical results given authenticate efficiency accuracy validity obtained results. Moreover, surface graphs plotted illustrate effect arrangement on behavior