Piecewise fractional interpolation with application to the Coupled System of Nonlinear Fractional Ordinary Differential Equations

In this paper, we consider the numerical method for the fractional differential equations. It is based on the piecewise fractional interpolants (PFIs), which is a new family of interpolants. We extend the technique to solve the Coupled system of fractional ordinary differential equations (FODEs) and present a predictor-corrector methods for the numerical solution of the coupled system of FODEs. By using the present method, we are able to solve efficiently the case that the solution of FODEs has lower smoothness. The stability and convergence of the present method is rigorously established. Some numerical examples are provided to confirm the theoretical claims.