Error estimate in fractional differential equations using multiquadratic radial basis functions

The purpose of this paper is to investigate the collocation method based on Multiquadric (MQ) radial basis functions (RBFs) for fractional differential equations (FDEs). In the process of doing this, a scattered data RBF interpolation is considered. A posterior error bound for the smooth solutions of FDEs in the proposed method is established in the L2 norm, using an alternate characterization of the native space. Numerical results are presented, which confirm the theoretical prediction of the convergence behavior of the proposed method.