A note on some recent results of the conformable fractional derivative

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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