@Article{AAMM-10-1440, author = {Yang , XingfaYang , YinChen , Yanping and Liu , Jie}, title = {Jacobi Spectral Collocation Method Based on Lagrange Interpolation Polynomials for Solving Nonlinear Fractional Integro-Differential Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {6}, pages = {1440--1458}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0038}, url = {http://global-sci.org/intro/article_detail/aamm/12718.html} }