(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
In this paper, we study a class of nonlinear fractional integro-differential equations. The fractional derivative is described in the Caputo sense. Using the properties of the Caputo derivative, we convert the fractional integro-differential equations into equivalent integral-differential equations of Volterra type with singular kernel, then we propose and analyze a spectral Jacobi-collocation approximation for nonlinear integro-differential equations of Volterra type. We provide a rigorous error analysis for the spectral methods, which shows that both the errors of approximate solutions and the errors of approximate fractional derivatives of the solutions decay exponentially in L^∞-norm and weighted L^2-norm.