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A New Diffusive Representation for Fractional Derivatives, Part I: Construction, Implementation and Numerical Examples

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Fractional Differential Equations (INDAM 2021)

Part of the book series: Springer INdAM Series ((SINDAMS,volume 50))

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Abstract

Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known variants of this approach is that they require the numerical approximation of some integrals over an unbounded integral whose integrand decays rather slowly, which implies that their numerical handling is difficult and costly. We present a novel variant of such a diffusive representation. This form also requires the numerical approximation of an integral over an unbounded domain, but the integrand decays much faster. This property allows to use well established quadrature rules with much better convergence properties.

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Author information

Authors and Affiliations

  1. Faculty of Applied Natural Sciences and Humanities, Technical University of Applied Sciences Würzburg-Schweinfurt, Schweinfurt, Germany

    Kai Diethelm

Authors
  1. Kai Diethelm
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Correspondence to Kai Diethelm .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Salerno, Fisciano, Salerno, Italy

    Angelamaria Cardone

  2. Department of Science and High Technology, University of Insubria, Como, Italy

    Marco Donatelli

  3. Department of Mathematics, University of Pisa, Pisa, Italy

    Fabio Durastante

  4. Department of Mathematics, University of Bari Aldo Moro, Bari, Italy

    Roberto Garrappa

  5. Department of Science and High Technology, University of Insubria, Como, Italy

    Mariarosa Mazza

  6. Department of Electrical and Information Engineering, Polytechnic University of Bari, Bari, Italy

    Marina Popolizio

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Diethelm, K. (2023). A New Diffusive Representation for Fractional Derivatives, Part I: Construction, Implementation and Numerical Examples. In: Cardone, A., Donatelli, M., Durastante, F., Garrappa, R., Mazza, M., Popolizio, M. (eds) Fractional Differential Equations. INDAM 2021. Springer INdAM Series, vol 50. Springer, Singapore. https://doi.org/10.1007/978-981-19-7716-9_1

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