Nonlinear fractional integro-differential reaction-diffusion equation via radial basis functions

This paper proposes a numerical method to deal with the nonlinear time-fractional integro-differential reaction-diffusion equation defined by the Caputo fractional derivative. In the proposed method, the space variable is eliminated by using finite difference θ-method to enjoy the stability condition. The method benefits from the radial basis function collocation method, in which the generalized thin plate splines (GTPS) radial basis functions are used. Therefore, it does not require any struggle to determine the shape parameter. The obtained results for some numerical examples reveal that the proposed technique is very effective, convenient and quite accurate to such considered problems.