A numerical study on the non-smooth solutions of the nonlinear weakly singular fractional Volterra integro-differential equations

The solutions of weakly singular fractional Volterra integro-differential equations involving the Caputo derivative typically have solutions whose derivatives are unbounded at the left end-point of the interval of integration. In this paper, we design an algorithm to prevail on this non-smooth behavior of solutions of the nonlinear fractional Volterra integro-differential equations with a weakly singular kernel. The convergence of the proposed method is investigated. The proposed scheme is employed to solve four numerical examples in order to test its efficiency and accuracy.