New Approach for Fractional Order Derivatives: Fundamentals and Analytic Properties

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dc.authoridKarci, Ali/0000-0002-8489-8617
dc.authorwosidKARCI, Ali/A-9604-2019
dc.authorwosidKarci, Ali/AAG-5337-2019
dc.contributor.authorKarci, Ali
dc.date.accessioned2024-08-04T20:44:35Z
dc.date.available2024-08-04T20:44:35Z
dc.date.issued2016
dc.departmentİnönü Üniversitesien_US
dc.description.abstractThe rate of change of any function versus its independent variables was defined as a derivative. The fundamentals of the derivative concept were constructed by Newton and l'Hopital. The followers of Newton and l'Hopital defined fractional order derivative concepts. We express the derivative defined by Newton and l'Hopital as an ordinary derivative, and there are also fractional order derivatives. So, the derivative concept was handled in this paper, and a new definition for derivative based on indefinite limit and l'Hopital's rule was expressed. This new approach illustrated that a derivative operator may be non-linear. Based on this idea, the asymptotic behaviors of functions were analyzed and it was observed that the rates of changes of any function attain maximum value at inflection points in the positive direction and minimum value (negative) at inflection points in the negative direction. This case brought out the fact that the derivative operator does not have to be linear; it may be non-linear. Another important result of this paper is the relationships between complex numbers and derivative concepts, since both concepts have directions and magnitudes.en_US
dc.identifier.doi10.3390/math4020030
dc.identifier.issn2227-7390
dc.identifier.issue2en_US
dc.identifier.scopus2-s2.0-85048402801en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://doi.org/10.3390/math4020030
dc.identifier.urihttps://hdl.handle.net/11616/98334
dc.identifier.volume4en_US
dc.identifier.wosWOS:000380042600010en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherMdpien_US
dc.relation.ispartofMathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectderivativesen_US
dc.subjectfractional calculusen_US
dc.subjectfractional order derivativesen_US
dc.titleNew Approach for Fractional Order Derivatives: Fundamentals and Analytic Propertiesen_US
dc.typeArticleen_US

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