TY - JOUR T1 - Jacobi Spectral Collocation Method Based on Lagrange Interpolation Polynomials for Solving Nonlinear Fractional Integro-Differential Equations AU - Yang , Xingfa AU - Yang , Yin AU - Chen , Yanping AU - Liu , Jie JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1440 EP - 1458 PY - 2018 DA - 2018/09 SN - 10 DO - http://doi.org/10.4208/aamm.OA-2018-0038 UR - https://global-sci.org/intro/article_detail/aamm/12718.html KW - Spectral method, nonlinear, fractional derivative, Volterra integro-differential equations, Caputo derivative. AB -

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.