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A Hilbert Space Approach to Fractional Differential Equations

  • We study fractional differential equations of Riemann–Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on R, we define fractional operators by means of a functional calculus using the Fourier transform. Main tools are extrapolation- and interpolation spaces. Main results are the existence and uniqueness of solutions and the causality of solution operators for non-linear fractional differential equations.

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Metadaten
Author:Kai Diethelm, Konrad Kitzing, Rainer Picard, Stefan Siegmund, Sascha Trostorff, Marcus Waurick
DOI:https://doi.org/10.1007/s10884-020-09932-6
Parent Title (English):Journal of Dynamics and Differential Equations
Document Type:Article
Language:English
Year of publication:2022
Release Date:2023/08/10
Volume:34
First Page:481
Last Page:504
Institutes and faculty:Fakultäten / Fakultät für angewandte Natur- und Geisteswissenschaften
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