A Hilbert space approach to fractional differential equations
Functional Analysis
2020-01-30 v2
Abstract
We study fractional differential equations of Riemann-Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on , 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.
Cite
@article{arxiv.1909.07662,
title = {A Hilbert space approach to fractional differential equations},
author = {Kai Diethelm and Konrad Kitzing and Rainer Picard and Stefan Siegmund and Sascha Trostorff and Marcus Waurick},
journal= {arXiv preprint arXiv:1909.07662},
year = {2020}
}