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

  • 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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Metadaten
Author:Kai Diethelm
DOI:https://doi.org/10.1007/978-981-19-7716-9_1
ISBN:978-981-19-7715-2
ISBN:978-981-19-7716-9
Parent Title (English):Fractional Differential Equations: Modeling, Discretization, and Numerical Solvers
Publisher:Springer
Place of publication:Singapore
Editor:Angelamaria Cardone, Marco Donatelli, Fabio Durastante, Roberto Garrappa, Mariarosa Mazza, Marina Popolizio
Document Type:Conference Proceeding
Language:English
Year of publication:2023
Release Date:2023/08/10
First Page:1
Last Page:15
Institutes and faculty:Fakultäten / Fakultät für angewandte Natur- und Geisteswissenschaften
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