A note on some recent results of the conformable fractional derivative

Year 2019, Volume: 3 Issue: 1, 11 - 17, 31.03.2019

O. Taghipour Birgani Sumit Chandok , Nebojsa Dedovic , Stojan Radenovic

https://doi.org/10.31197/atnaa.482525

Cited By: 12

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 fractional derivative; fractional derivative; fractional integral; Riemann-Liouvelle definition; Caputo definition; fractional differential equations

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