Fractional Sobolev Space on Time Scales and Its Application to a Fractional Boundary Value Problem on Time Scales

By the concept of fractional derivative of Riemann-Liouville on time scales, we first introduce fractional Sobolev spaces, characterize them, define weak fractional derivatives, and show that they coincide with the Riemann-Liouville ones on time scales. Then, we prove equivalence of some norms in th...

Full description

Saved in:
Bibliographic Details
Published in:Journal of function spaces 2022-01, Vol.2022, p.1-20
Main Authors: Hu, Xing, Li, Yongkun
Format: Article
Language:English
Subjects:
Applied mathematics
Boundary value problems
Imbeddings
Mathematical functions
Norms
Sobolev space
Time
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:By the concept of fractional derivative of Riemann-Liouville on time scales, we first introduce fractional Sobolev spaces, characterize them, define weak fractional derivatives, and show that they coincide with the Riemann-Liouville ones on time scales. Then, we prove equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, separability, and some imbeddings. Finally, as an application, by constructing an appropriate variational setting, using fibering mapping and Nehari manifolds, the existence of weak solutions for a class of fractional boundary value problems on time scales is studied, and a result of the existence of weak solutions for this problem is obtained.
ISSN:2314-8896
2314-8888
DOI:10.1155/2022/7149356