Runge–Kutta convolution quadrature methods with convergence and stability analysis for nonlinear singular fractional integro-differential equations

Abstract The main concern of this paper is to develop and analyze the high-order Runge–Kutta convolution quadrature (RKCQ) method for obtaining the numerical solution of nonlinear fractional integro-differential equations (FIDEs) with weakly singular kernels. We first study the existence and uniqueness of solutions for the original problem. Then, the convergence and stability results of the RKCQ method are obtained. Finally, some numerical experiments are reported to illustrate the effectiveness of the proposed schemes.