Fractional retarded differential equations and their numerical solution via a multistep collocation method

In this paper, we consider the nonlinear fractional retarded differential equations (FRDE). We extend the results of the existence and uniqueness of the solution, the propagation of derivative discontinuities and the dependence of the solution on the parameters of the equation. Next, we develop an efficient multistep collocation method for solving this type of equations. The proposed scheme is especially suited for FRDEs with piecewise smooth solutions, due to its essential feature of local approximations on subintervals. The stability of the scheme is accessed, and the convergence analysis is studied for functions in appropriate Sobolev spaces. Numerical results confirm the spectral accuracy and the stability of the proposed method for large domain calculations. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.