A New Fundamental and Numerical Method for the Fractional Partial Differential Equations

Abstract

Fractional order has the characteristics of memory and non-locality and it is different with integer order. Therefore, fractional differential equations can be used to describe some abnormal natural phenomena. At the same time, how to solve the fractional order partial differential equation and differential equations with fractional order has become a very important research field. Besides analytic solution, it is also important to investigate the numerical methods for fractional differential equations. In the paper, fundamental solution of the time fractional partial differential equation has been deduced, which is derived by Furrier transform and Laplace transform. According to the simulation, there is little difference between numerical solution and the exact solution when the solution is the time variable function. The results show the validity of the method.