A study of fractional order Ambartsumian equation involving exponential decay kernel

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dc.authoridUllah, Aman/0000-0003-4021-3599
dc.authoridAhmad, Shabir/0000-0002-5610-6248
dc.authoridde la Sen, manuel/0000-0001-9320-9433
dc.contributor.authorAhmad, Shabir
dc.contributor.authorUllah, Aman
dc.contributor.authorAkgul, Ali
dc.contributor.authorDe la Sen, Manuel
dc.date.accessioned2024-12-24T19:33:59Z
dc.date.available2024-12-24T19:33:59Z
dc.date.issued2021
dc.departmentSiirt Üniversitesi
dc.description.abstractRecently, non-singular fractional operators have a significant role in the modeling of real-world problems. Specifically, the Caputo-Fabrizio operators are used to study better dynamics of memory processes. In this paper, under the non-singular fractional operator with exponential decay kernel, we analyze the Ambartsumian equation qualitatively and computationally. We deduce the result of the existence of at least one solution to the proposed equation through Krasnoselskii's fixed point theorem. Also, we utilize the Banach fixed point theorem to derive the result concerned with unique solution. We use the concept of functional analysis to show that the proposed equation is Ulam-Hyers and Ulam-Hyers-Rassias stable. We use an efficient analytical approach to compute a semi-analytical solution to the proposed problem. The convergence of the series solution to an exact solution is proved through non-linear analysis. Lastly, we present the solution for different fractional orders.
dc.description.sponsorshipBasque Government [IT120719]
dc.description.sponsorshipThe authors are grateful to the Basque Government by Grant IT120719.
dc.identifier.doi10.3934/math.2021580
dc.identifier.endpage9997
dc.identifier.issn2473-6988
dc.identifier.issue9
dc.identifier.scopus2-s2.0-85109010978
dc.identifier.scopusqualityQ1
dc.identifier.startpage9981
dc.identifier.urihttps://doi.org/10.3934/math.2021580
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8370
dc.identifier.volume6
dc.identifier.wosWOS:000683418700028
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherAmer Inst Mathematical Sciences-Aims
dc.relation.ispartofAims Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectAmbartsumian equation
dc.subjectUlam-Hyres-Rassias stable
dc.subjectnon-linear analysis
dc.titleA study of fractional order Ambartsumian equation involving exponential decay kernel
dc.typeArticle

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