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

Künye