Revised and Generalized Results of Averaging Principles for the Fractional Case

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dc.contributor.authorLiaqat, Muhammad Imran
dc.contributor.authorKhan, Zareen A.
dc.contributor.authorConejero, J. Alberto
dc.contributor.authorAkgul, Ali
dc.date.accessioned2024-12-24T19:33:33Z
dc.date.available2024-12-24T19:33:33Z
dc.date.issued2024
dc.departmentSiirt Üniversitesi
dc.description.abstractThe averaging principle involves approximating the original system with a simpler system whose behavior can be analyzed more easily. Recently, numerous scholars have begun exploring averaging principles for fractional stochastic differential equations. However, many previous studies incorrectly defined the standard form of these equations by placing epsilon in front of the drift term and epsilon in front of the diffusion term. This mistake results in incorrect estimates of the convergence rate. In this research work, we explain the correct process for determining the standard form for the fractional case, and we also generalize the result of the averaging principle and the existence and uniqueness of solutions to fractional stochastic delay differential equations in two significant ways. First, we establish the result in Lp space, generalizing the case of p=2. Second, we establish the result using the Caputo-Katugampola operator, which generalizes the results of the Caputo and Caputo-Hadamard derivatives.
dc.description.sponsorshipPrincess Nourah bint Abdulrahman University Researchers Supporting Project; Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia; [PNURSP2024R8]
dc.description.sponsorshipThis research was funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R8), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
dc.identifier.doi10.3390/axioms13110732
dc.identifier.issn2075-1680
dc.identifier.issue11
dc.identifier.urihttps://doi.org/10.3390/axioms13110732
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8193
dc.identifier.volume13
dc.identifier.wosWOS:001366731000001
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.language.isoen
dc.publisherMdpi
dc.relation.ispartofAxioms
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectgeneralized fractional operator
dc.subjectstochastic fractional differential equations
dc.subjectexistence and uniqueness
dc.titleRevised and Generalized Results of Averaging Principles for the Fractional Case
dc.typeArticle

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