Abstract
We establish some properties of the bilateral Riemann–Liouville fractional derivative Ds. We set the notation, and study the associated Sobolev spaces of fractional order s, denoted by Ws,1(a,b), and the fractional bounded variation spaces of fractional order s, denoted by BVs(a,b). Examples, embeddings and compactness properties related to these spaces are addressed, aiming to set a functional framework suitable for fractional variational models for image analysis.
Funder
Ministry of Education, Universities and Research
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference36 articles.
1. Bilateral Riemann-Liouville Fractional Sobolev spaces;Leaci;Note Mat.,2021
2. A note on Riemann-Liouville fractional Sobolev spaces
3. The fractional variation and the precise representative of BVα,p functions;Comi;arXiv,2021
4. A distributional approach to fractional Sobolev spaces and fractional variation: Existence of blow-up
5. A distributional approach to fractional Sobolev spaces and fractional variation: Asymptotics I;Comi;arXiv,2019
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献