"Conformable derivative: A derivative associated to the Riemann-Stieltj" by Abdon Atangana, Ali Akgu ̈l et al.

Progress in Fractional Differentiation & Applications

Article Title

Conformable derivative: A derivative associated to the Riemann-Stieltjes integral

Authors

Abdon Atangana, Institute for Groundwater Studies, Faculty of Natural and Agricultural Science, University of Free State, 9300, Bloemfontein, South Africa\\ Department of Medical Research, China, Medical University Hospital, China, Medical University, Taichung, Taiwan Follow
Ali Akgu ̈l, Siirt University, Art and Science Faculty, Department of Mathematics, TR-56100 Siirt, TurkeyFollow
Muhammad Altaf Khan, Institute for Groundwater Studies, Faculty of Natural and Agricultural Science, University of Free State, 9300, Bloemfontein, South AfricaFollow
Rabha Waell Ibrahim, IEEE: 94086547, Kuala Lumpur, 59200, MalaysiaFollow

Author Country (or Countries)

Turkey

Abstract

In mathematics, the Riemann-Stieltjes integral 􏰝 f(t)dg(t) is known to be the more general version of the well-known Riemann integral that is used in classical integral calculus. This integral has found application in several fields. However, there is no clear derivative associate to the generalized integral, except the concept of global derivative that was suggested very recently. Nevertheless, a more generalized differential operator called conformable derivative was suggested and many concerns have been raised as what such operator cannot be considered as derivative. In this paper, we proved that not only the operator is a derivative but a derivative associate to the well-known Riemann-Stieltjes integral. We have in addition present some applications of the conformable derivative in image processing and dynamical processes including chaos and epidemiology.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/080211

Recommended Citation

Atangana, Abdon; Akgu ̈l, Ali; Altaf Khan, Muhammad; and Waell Ibrahim, Rabha (2022) "Conformable derivative: A derivative associated to the Riemann-Stieltjes integral," Progress in Fractional Differentiation & Applications: Vol. 8: Iss. 2, Article 11.
DOI: http://dx.doi.org/10.18576/pfda/080211
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol8/iss2/11

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