- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 3 Issue: 1
- A note on some recent results of the conformable fractional derivative
A note on some recent results of the conformable fractional derivative
Authors : O. Taghipour BİRGANİ, Sumit CHANDOK, Nebojsa DEDOVİC, Stojan RADENOVİC
Pages : 11-17
Doi:10.31197/atnaa.482525
View : 4 | Download : 9
Publication Date : 2019-03-31
Article Type : Other
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