A Quadrature Tau Method for Solving Fractional Integro-differential Equations in the Caputo Sense


Authors

A. Yousefi - Department of Computer Science, Faculty of Mathematical Science and Computer, Kharazmi University, Tehran, Iran T. Mahdavi Rad - Department of Mathematics, Arak branch, Islamic Azad University, Arak, Iran. S. G. Shafiei - Department of Computer Science, Faculty of Mathematical Science and Computer, Kharazmi University, Tehran, Iran


Abstract

In this article, we develop a direct solution technique for solving fractional integro-differential equations (FIDEs) in the Caputo sense using a quadrature shifted Legendre Tau (Q-SLT) method. The spatial approximation is based on shifted Legendre polynomials. A new formula expressing explicitly any fractional-order derivatives of shifted Legendre polynomials of any degree in terms of shifted Legendre polynomials themselves is proved. Extension of the Tau method for FIDEs is treated using the shifted Legendre–Gauss–Lobatto quadrature. The method is illustrated by considering some examples whose exact solutions are available. The results obtained through this method are stable and comparable with the existing methods for a variety of problems with practical applications.


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ISRP Style

A. Yousefi, T. Mahdavi Rad, S. G. Shafiei, A Quadrature Tau Method for Solving Fractional Integro-differential Equations in the Caputo Sense, Journal of Mathematics and Computer Science, 15 (2015), no. 2, 97-107

AMA Style

Yousefi A., Rad T. Mahdavi, Shafiei S. G., A Quadrature Tau Method for Solving Fractional Integro-differential Equations in the Caputo Sense. J Math Comput SCI-JM. (2015); 15(2):97-107

Chicago/Turabian Style

Yousefi, A., Rad, T. Mahdavi, Shafiei, S. G.. "A Quadrature Tau Method for Solving Fractional Integro-differential Equations in the Caputo Sense." Journal of Mathematics and Computer Science, 15, no. 2 (2015): 97-107


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