A note on some recent results of the conformable fractional derivative

Open Access

Original research article

Author(s):

Omid T. Birgani^a, Sumit Chandok^b, Nebojša Dedović^c, Stojan Radenović^d

^aSchool of Mathematics, Iran University of Science and Technology, Tehran, Iran
^bSchool of Mathematics, Thapar University, Patiala–147004, India
^cFaculty of Agriculture, University of Novi Sad, Novi Sad, Serbia
^dDepartment of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

Advances in the Theory of Nonlinear Analysis and its Applications 3(1), 11-17.

Received: December 14, 2018

Accepted: December 21, 2018

Published: December 30, 2018

Abstract

In this note, we discuss, improve and complement some recent results of the conformable fractional derivative introduced and established by Katugampola [arxiv:1410.6535v1] and Khalil et al. [J. Comput. Appl. Math. 264(2014) 65-70]. Among other things we show that each function f defined on (a,b), a>0 has a conformable fractional derivative (CFD) if and only if it has a classical first derivative. At the end of the paper, we prove the Rolle’s, Cauchy, Lagrange’s and Darboux’s theorem in the context of Conformable Fractional Derivatives.

Keywords: Conformable derivative, Darboux’s theorem, differential equations.

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APA Style

Birgani, O. T., Chandok, S., Dedovic, N., & Radenovic, S. (2019). A note on some recent results of the conformable fractional derivative. Advances in the Theory of Nonlinear Analysis and its Application, 3(1), 11-17.