Calculus of Variations and Geometric Measure Theory

A. Leaci - F. Tomarelli

Bilateral Riemann-Liouville fractional Sobolev spaces

created by leaci on 11 Oct 2021


Accepted Paper

Inserted: 11 oct 2021
Last Updated: 11 oct 2021

Journal: Note di Matematica
Year: 2021


We establish some notation and properties of the bilateral Riemann-Liouville fractional derivative $D^s$: We introduce the associated Sobolev spaces of fractional order $s$, denoted by $W^{s,1}(a,b)$, and the Bounded Variation spaces of fractional order $s$, denoted by $BV^s(a,b)$: these spaces are studied with the aim of providing a suitable functional framework for fractional variational models in image analysis.

Keywords: Fractional Calculus, Fractional Sobolev and BV Spaces.