A Hilbert Space Approach to Fractional Differential Equations

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

Abstract

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.

Details

OriginalspracheEnglisch
Seiten (von - bis)481-504
Seitenumfang24
FachzeitschriftJournal of dynamics and differential equations
Jahrgang34
Ausgabenummer1
PublikationsstatusVeröffentlicht - März 2022
Peer-Review-StatusJa

Externe IDs

ORCID /0000-0003-0967-6747/work/150327290

Schlagworte

ASJC Scopus Sachgebiete

Schlagwörter

  • Caputo derivative, Causality, Fractional differential equations, Riemann–Liouville derivative