Numerical Solution of a Family of Fractional Differential Equations by Use of RBF Method

Radial basis function (RBF) interpolation methods are theoretically spectrally accurate. In applications this accuracy is seldom realized due to the necessity of solving a very poorly conditioned linear system to evaluate the methods. Some numerical methods such as Adomian decomposition method and Homotopy perturbation method works for a family of fractional differential equations. In this work, we approximate the exact solution by use of Radial Basis Functions method (RBF). It is important to note that the RBF method finally converges to a linear system and we can solve that system very easily by some Math Microsoft such as MAPLE, MATLAB or MATHEMATICA. Our results show the accurate of this method for these kinds of differential equations.