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.
Author: | Kai Diethelm, Konrad Kitzing, Rainer Picard, Stefan Siegmund, Sascha Trostorff, Marcus Waurick |
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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 |