Concluding remarks
Fractional differential equations have found applications in many different fields. In this paper, the operational matrices of derivative and fractional Riemann-Liouville integration with Legendre polynomials have been successfully applied to compute approximate solutions of some fractional partial differential equations. As test examples, the linear time fractional Klein-Gordan equation, dissipative Klein-Gordan equation and diffusion-wave equation were considered. The numerical results demonstrated that the presented scheme provide approximate solutions in an acceptable agreement with exact solutions. Moreover, results indicated that the propounded approach leads to a better approximation as the order of Legendre polynomials increases. For future works this work can also be generalized and verified for more complicated linear, nonlinear or high dimensions problems. It is worth mentioning that the numerical solutions were obtained using Mathematica 11 software.
