On the Set-Valued Katugampola Fractional Integral: Properties and Regular Selections

Abstract

In this paper, we develop a theory of generalized fractional integration for set-valued mappings for the Katugampola fractional integral, which unifies the classical Riemann-Liouville and Hadamard fractional integrals. The Katugampola fractional integral of a set valued mapping is studied using integrable selections. We study its properties with respect to the Hausdorff metric on the space of nonempty compact subsets of R and several fundamental analytical characteristics including convexity, boundedness and continuity are preserved under Katugampola fractional integration. Furthermore, we establish that both bounded variation and Lipschitz regularity of a set-valued mapping are preserved under its Katugampola fractional integral. We investigate the existence of regular selections associated with the Katugampola fractional integral and show that whenever the original set valued mapping admits a selection with a specified regularity property, the corresponding Katugampola fractional integral does as well.

Regular integral models of Shimura varieties and a conjecture of Pappas
Jie Yang, Ioannis Zachos, Zhihao Zhao
arXiv7 Oct 2026PreprintarXiv licenceFull textAlgebra & number theoryarXiv
Integral Harnack inequality and expansion of positivity for fractional porous medium equation
Filippo Maria Cassanello, Filomena De Filippis, Calvin Stanko
arXiv7 Oct 2026PreprintCC BY 4.0Full textAnalysis & PDEsarXiv
The Dirichlet problem with boundary data of fractional smoothness in domains with Ahlfors regular boundary
Ariel Barton, Svitlana Mayboroda, Alberto Pacati
arXiv5 Oct 2026PreprintarXiv licenceFull textAnalysis & PDEsarXiv
Structural Characterizations and Algebraic Realizations of a Family of Regular Integral Graphs
Tapa Manna, Supriyo Dutta, Baby Bhattacharya
arXiv22 Sep 2026PreprintCC BY 4.0Full textAlgebra & number theory Combinatorics & discrete mathematicsarXiv
Almost L^∞-stability of the Ritz projection for the integral fractional Laplacian with 0<s≤ 1/2
Jia Li, Shuonan Wu
arXiv15 Oct 2026PreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv

Cite

BibTeX RIS

BibTeX

@misc{kaur2026setvalued,
  title = {{On the Set-Valued Katugampola Fractional Integral: Properties and Regular Selections}},
  author = {Parneet Kaur and Rattan Lal and Ankit Kumar},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00702},
  eprint = {2609.00702},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00702},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - On the Set-Valued Katugampola Fractional Integral: Properties and Regular Selections
AU  - Parneet Kaur
AU  - Rattan Lal
AU  - Ankit Kumar
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00702
UR  - https://arxiv.org/abs/2609.00702
AB  - In this paper, we develop a theory of generalized fractional integration for set-valued mappings for the Katugampola fractional integral, which unifies the classical Riemann-Liouville and Hadamard fractional integrals. The Katugampola fractional integral of a set valued mapping is studied using integrable selections. We study its properties with respect to the Hausdorff metric on the space of nonempty compact subsets of R and several fundamental analytical characteristics including convexity, boundedness and continuity are preserved under Katugampola fractional integration. Furthermore, we establish that both bounded variation and Lipschitz regularity of a set-valued mapping are preserved under its Katugampola fractional integral. We investigate the existence of regular selections associated with the Katugampola fractional integral and show that whenever the original set valued mapping admits a selection with a specified regularity property, the corresponding Katugampola fractional integral does as well.
ER  -

Abstract

Related

Cite