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http://dx.doi.org/10.4134/JKMS.2014.51.1.203

SPECTRAL-COLLOCATION METHOD FOR FRACTIONAL FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS  

Yang, Yin (Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University)
Chen, Yanping (School of Mathematical Sciences South China Normal University)
Huang, Yunqing (Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University)
Publication Information
Journal of the Korean Mathematical Society / v.51, no.1, 2014 , pp. 203-224 More about this Journal
Abstract
We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of Fredholm-Volterra type. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in $L^{\infty}$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.
Keywords
spectral Jacobi-collocation method; fractional order Fredholm integro-differential equations; Caputo derivative;
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