@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 = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2018-0038},
url = {http://global-sci.org/intro/article_detail/aamm/12718.html}
}