TY  - JOUR
T1  - A note on some recent results of the conformable fractional derivative
AU  - Birgani, O. Taghipour
AU  - Dedovic, Nebojsa
AU  - Chandok, Sumit
AU  - Radenovic, Stojan
PY  - 2019
DA  - March
DO  - 10.31197/atnaa.482525
JF  - Advances in the Theory of Nonlinear Analysis and its Application
JO  - ATNAA
PB  - Erdal KARAPINAR
WT  - DergiPark
SN  - 2587-2648
SP  - 11
EP  - 17
VL  - 3
IS  - 1
LA  - en
AB  - In this note, we discuss, improve and complement some recent results of theconformable 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 hasa 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 ConformableFractional Derivatives.
KW  - Conformable fractional derivative; fractional derivative; fractional integral; Riemann-Liouvelle definition; Caputo definition; fractional differential equations
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UR  - https://doi.org/10.31197/atnaa.482525
L1  - https://dergipark.org.tr/en/download/article-file/612536
ER  -