Step forward on nonlinear differential equations with the Atangana-Baleanu derivative: Inequalities, existence, uniqueness and method

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dc.contributor.authorAtangana, Abdon
dc.contributor.authorAraz, Seda Igret
dc.date.accessioned2024-12-24T19:25:28Z
dc.date.available2024-12-24T19:25:28Z
dc.date.issued2023
dc.departmentSiirt Üniversitesi
dc.description.abstractIn this study, we have found new results related to the fractional derivatives, integrals, and corresponding nonlinear ordinary differential and integral equations of Atangana-Baleanu. A comment on the initial condition problem when working with ordinary differential equations with the Atangana-Baleanu fractional derivative introduced the paper. We have developed a variety of new inequalities that are similar to the Gronwall and generalized-Gronwall inequalities using some criteria for the evaluation. The linear growth condition was utilized to obtain several new inequalities after the interval and initial condition dependency were established. We demonstrated a Picard-Tonelli predictor-corrector integration for the Atangana-Baleanu fractional nonlinear differential equation's local solution. We established three distinct proofs of uniqueness using the Kransorsel'skii-Krein, Kooi's, and Lipschitz conditions. The Nystrom midpoint approach has also been expanded to include nonlinear ordinary differential equations with the Atangana-Baleanu derivative; hence, the case of Caputo is straightforward. To assess the effectiveness of this method, some theoretical analyses and some practical cases were provided.
dc.identifier.doi10.1016/j.chaos.2023.113700
dc.identifier.issn0960-0779
dc.identifier.issn1873-2887
dc.identifier.scopus2-s2.0-85163405745
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1016/j.chaos.2023.113700
dc.identifier.urihttps://hdl.handle.net/20.500.12604/6425
dc.identifier.volume173
dc.identifier.wosWOS:001040309900001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherPergamon-Elsevier Science Ltd
dc.relation.ispartofChaos Solitons & Fractals
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectInequalities
dc.subjectNonlinear differential equations
dc.subjectExistence and uniqueness
dc.subjectAtangana-Baleanu derivative
dc.subjectNumerical scheme
dc.titleStep forward on nonlinear differential equations with the Atangana-Baleanu derivative: Inequalities, existence, uniqueness and method
dc.typeArticle

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