TY - JOUR A1 - Diethelm, Kai A1 - Kitzing, Konrad A1 - Picard, Rainer A1 - Siegmund, Stefan A1 - Trostorff, Sascha A1 - Waurick, Marcus T1 - A Hilbert Space Approach to Fractional Differential Equations T2 - Journal of Dynamics and Differential Equations N2 - 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. Y1 - 2022 UR - https://opus4.kobv.de/opus4-fhws/frontdoor/index/index/docId/3226 VL - 34 SP - 481 EP - 504 ER -