What Is A Fractional Derivative? (Vol 293, Pg 4, 2015)

There is a debate among contemporary mathematicians about what it really means by a fractional derivative. The question arose as a consequence of introducing a 'new' definition of a fractional derivative in [1]. In a reply, Ortigueira and Machado [2] came up with several very important criteria to determine whether a given derivative is a fractional derivative. According to their criterion, the new fractional derivative, called conformable fractional derivative, introduced by Khalil et al. [1] turns out not to be a fractional derivative, but rather a controlled or conformable derivative. In proving the claim the authors in [2] use an example [2, p. 6]. It turns out that the explanation given there needs some corrections and it is the sole purpose of this note. (C) 2016 Elsevier Inc. All rights reserved.