SPECTRAL-COLLOCATION METHOD FOR FRACTIONAL FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

Title & Authors
SPECTRAL-COLLOCATION METHOD FOR FRACTIONAL FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS
Yang, Yin; Chen, Yanping; Huang, Yunqing;

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 $\small{L^{\infty}}$ norm and weighted $\small{L^2}$-norm. The numerical examples are given to illustrate the theoretical results.
Keywords
spectral Jacobi-collocation method;fractional order Fredholm integro-differential equations;Caputo derivative;
Language
English
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