New Approach for Fractional Order Derivatives: Fundamentals and Analytic Properties
Küçük Resim Yok
Tarih
2016
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Mdpi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
The 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.
Açıklama
Anahtar Kelimeler
derivatives, fractional calculus, fractional order derivatives
Kaynak
Mathematics
WoS Q Değeri
N/A
Scopus Q Değeri
Q2
Cilt
4
Sayı
2