- Advances in the Theory of Nonlinear Analysis and its Application
- Volume: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 : 26 | Download : 15
Publication Date : 2019-03-31
Article Type : Other Papers
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. 264insert ignore into journalissuearticles values(2014); 65-70]. Among other things we show that each function $f$ defined on $insert ignore into journalissuearticles values(a,b);$ , $a>0$ has a conformable fractional derivative insert ignore into journalissuearticles values(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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