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A Legendre collocation method for fractional integro-differential equations. (English) Zbl 1271.65157

Summary: A numerical method for solving the linear and non-linear fractional integro-differential equations of Volterra type is presented. The fractional derivative is described in the Caputo sense. The method is based upon Legendre approximations. The properties of Legendre polynomials together with the Gaussian integration method are utilized to reduce the fractional integro-differential equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the presented technique and a comparison is made with existing results.

MSC:

65R20 Numerical methods for integral equations
26A33 Fractional derivatives and integrals
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