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arXiv · 1909.07662

A Hilbert space approach to fractional differential equations

Kai Diethelm·Konrad Kitzing·Rainer Picard·Stefan Siegmund·Sascha Trostorff·Marcus Waurick
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Abstract

We study fractional differential equations of Riemann-Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on $\mathbb{R}$, 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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Kai Diethelm, Konrad Kitzing, Rainer Picard, Stefan Siegmund, Sascha Trostorff, Marcus Waurick. 2019-09-17. A Hilbert space approach to fractional differential equations. https://arxiv.org/abs/1909.07662

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