Qualitative Analysis of Stochastic Caputo-Katugampola Fractional Differential Equations

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dc.contributor.authorKhan, Zareen A.
dc.contributor.authorLiaqat, Muhammad Imran
dc.contributor.authorAkgul, Ali
dc.contributor.authorConejero, J. Alberto
dc.date.accessioned2024-12-24T19:33:33Z
dc.date.available2024-12-24T19:33:33Z
dc.date.issued2024
dc.departmentSiirt Üniversitesi
dc.description.abstractStochastic pantograph fractional differential equations (SPFDEs) combine three intricate components: stochastic processes, fractional calculus, and pantograph terms. These equations are important because they allow us to model and analyze systems with complex behaviors that traditional differential equations cannot capture. In this study, we achieve significant results for these equations within the context of Caputo-Katugampola derivatives. First, we establish the existence and uniqueness of solutions by employing the contraction mapping principle with a suitably weighted norm and demonstrate that the solutions continuously depend on both the initial values and the fractional exponent. The second part examines the regularity concerning time. Third, we illustrate the results of the averaging principle using techniques involving inequalities and interval translations. We generalize these results in two ways: first, by establishing them in the sense of the Caputo-Katugampola derivative. Applying condition beta=1, we derive the results within the framework of the Caputo derivative, while condition beta -> 0+ yields them in the context of the Caputo-Hadamard derivative. Second, we establish them in Lp space, thereby generalizing the case for p=2.
dc.description.sponsorshipPrincess Nourah bint Abdulrahman University [PNURSP2024R8]; Princess Nourah bint Abdulrahman University Researchers Supporting Project; Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia
dc.description.sponsorshipPrincess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R8). Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
dc.identifier.doi10.3390/axioms13110808
dc.identifier.issn2075-1680
dc.identifier.issue11
dc.identifier.urihttps://doi.org/10.3390/axioms13110808
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8194
dc.identifier.volume13
dc.identifier.wosWOS:001366850800001
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.subjectpantograph terms
dc.subjectCaputo-Katugampola derivatives
dc.subjectwell-posedness
dc.subjectaveraging principle
dc.titleQualitative Analysis of Stochastic Caputo-Katugampola Fractional Differential Equations
dc.typeArticle

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