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Fractional Calculus and Applied Analysis

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Fractional calculus and Sinc methods

1Mathematics Department, German University in Cairo, New Cairo City, Egypt

3Department of Mathematical Physics, University of Ulm, Albert-Einstein-Allee 11, D - 89069, Ulm, Germany

2School of Computing, University of Utah, 3414 Merrill Engineering Bldg., Salt Lake City, UT, 84112, USA

© 2011 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citation Information: Fractional Calculus and Applied Analysis. Volume 14, Issue 4, Pages 568–622, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: 10.2478/s13540-011-0035-3, September 2011

Publication History

Published Online:
2011-09-29

Abstract

Fractional integrals, fractional derivatives, fractional integral equations, and fractional differential equations are numerically solved by Sinc methods. Sinc methods are able to deal with singularities of the weakly singular integral equations of Riemann-Liouville and Caputo type. The convergence of the numerical method is numerically examined and shows exponential behavior. Different examples are used to demonstrate the effective derivation of numerical solutions for different types of fractional differential and integral equations, linear and non-linear ones. Equations of mixed ordinary and fractional derivatives, integro-differential equations are solved using Sinc methods. We demonstrate that the numerical calculation needed in fractional calculus can be gained with high accuracy using Sinc methods.

MSC: Primary 65-XX, 45-XX, 97-XX; Secondary 65D15, 45E10, 44A35, 97N50

Keywords: Sinc method; fractional calculus; approximation

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