Iterative solutions for nonlinear equations via fractional derivatives: adaptations and advances

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dc.authoridAli, Nasir/0000-0003-4116-9673
dc.authoridTesgera Tolasa, Fikadu/0000-0003-0742-6779
dc.contributor.authorAli, Nasir
dc.contributor.authorWaseem, Muhammad
dc.contributor.authorSafdar, Maimoona
dc.contributor.authorAkgul, Ali
dc.contributor.authorTolasa, Fikadu Tesgera
dc.date.accessioned2024-12-24T19:28:27Z
dc.date.available2024-12-24T19:28:27Z
dc.date.issued2024
dc.departmentSiirt Üniversitesi
dc.description.abstractIn recent years, the utilization of fractional calculus has witnessed a notable surge across various scientific and engineering domains. This manuscript delves into the exploration of adapted iterative techniques tailored for solving nonlinear equations, capitalizing on the diverse range of derivatives available for addressing different problem contexts. We scrutinize previously developed iterative methods, enhancing their efficacy by introducing an auxiliary parameter to the root search process for nonlinear equations (NLE), alongside a fixed order of fractional derivatives. The selection of the auxiliary parameter is confined to the interval (0,1] for convenience. A thorough convergence analysis is conducted, employing a fractional power series expansion of f(x) in terms of fractional derivatives. Subsequently, a series of NLEs is solved to showcase and contrast the efficiency of our proposed methods with established iterative techniques. This refined abstract aims to succinctly elucidate the objectives and contributions of our study, providing readers with a clearer understanding of the manuscript's scope and significance.
dc.identifier.doi10.1080/27690911.2024.2333816
dc.identifier.issn2769-0911
dc.identifier.issue1
dc.identifier.scopus2-s2.0-85189073282
dc.identifier.scopusqualityN/A
dc.identifier.urihttps://doi.org/10.1080/27690911.2024.2333816
dc.identifier.urihttps://hdl.handle.net/20.500.12604/7062
dc.identifier.volume32
dc.identifier.wosWOS:001192228100001
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherTaylor & Francis Ltd
dc.relation.ispartofApplied Mathematics in Science and Engineering
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectNonlinear equation
dc.subjectfractional derivatives
dc.subjectiterative scheme
dc.subjectconvergence
dc.subjectengineering models
dc.titleIterative solutions for nonlinear equations via fractional derivatives: adaptations and advances
dc.typeArticle

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