Numerical solution of fractional ordinary and partial differential equations by an operational technique

The purpose of this paper is to present a numerical technique for solving the fractional ordinary differential equations (FODEs) and fractional partial differential equations (FPDEs). The proposed technique is based on operational Tau method (OTM). The main idea behind the OTM is to convert the desired problem to some operational matrices. The development of the technique for FODEs and FPDEs is considered. Some linear and nonlinear experiments are applied to solve 1D and 2D fractional differential equations (FDEs) and a comparison is made between the proposed technique and the other methods. The results demonstrate the accuracy and the validity of the new technique.