A Study of Some Generalized Results of Neutral Stochastic Differential Equations in the Framework of Caputo–Katugampola Fractional Derivatives

Autor:	Abdelhamid Mohammed Djaouti, Zareen A. Khan, Muhammad Imran Liaqat, Ashraf Al-Quran
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	fractional calculus inequalities neutral stochastic differential equations averaging principle Caputo–Katugampola derivatives Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 11, p 1654 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12111654
Popis:	Inequalities serve as fundamental tools for analyzing various important concepts in stochastic differential problems. In this study, we present results on the existence, uniqueness, and averaging principle for fractional neutral stochastic differential equations. We utilize Jensen, Burkholder–Davis–Gundy, Grönwall–Bellman, Hölder, and Chebyshev–Markov inequalities. We generalize results in two ways: first, by extending the existing result for p=2 to results in the Lp space; second, by incorporating the Caputo–Katugampola fractional derivatives, we extend the results established with Caputo fractional derivatives. Additionally, we provide examples to enhance the understanding of the theoretical results we establish.
Databáze:	Directory of Open Access Journals
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