Generalized Grönwall Inequality and Ulam–Hyers Stability in ℒ p Space for Fractional Stochastic Delay Integro-Differential Equations

Abdelhamid Mohammed Djaouti () and Muhammad Imran Liaqat
Additional contact information
Abdelhamid Mohammed Djaouti: Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, Al Hofuf 31982, Saudi Arabia
Muhammad Imran Liaqat: Department of Mathematics, National College of Business Administration & Economics, Lahore 54000, Pakistan

Mathematics, 2025, vol. 13, issue 8, 1-23

Abstract: In this work, we derive novel theoretical results concerning well-posedness and Ulam–Hyers stability. Specifically, we investigate the well-posedness of Caputo–Katugampola fractional stochastic delay integro-differential equations. Additionally, we develop a generalized Grönwall inequality and apply it to prove Ulam–Hyers stability in L p space. Our findings generalize existing results for fractional derivatives and space, as we formulate them in the Caputo–Katugampola fractional derivative and L p space. To support our theoretical results, we present an illustrative example.

Keywords: well-posedness; Ulam–Hyers stability; generalized Grönwall inequality; Hölder’s inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/8/1252/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/8/1252/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:8:p:1252-:d:1632219

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().