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Fractional calculus and Sinc methods

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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.

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Authors and Affiliations

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

    Gerd Baumann

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

    Gerd Baumann

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

    Frank Stenger

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  1. Gerd Baumann
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  2. Frank Stenger
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Correspondence to Gerd Baumann.

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Baumann, G., Stenger, F. Fractional calculus and Sinc methods. fcaa 14, 568–622 (2011). https://doi.org/10.2478/s13540-011-0035-3

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