Correction to "What is a fractional derivative?" by Ortigueira and Machado [Journal of Computational Physics, Volume 293, 15 July 2015, Pages 4-13. Special issue on Fractional PDEs]

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 a reply Ortigueira and Machado [1] 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. [2] turns out not to be a fractional derivative, but rather a controlled derivative. In proving the claim the authors in [1] use an example [1, page 6]. It turns out that the explanation given there needs some corrections and it is the sole purpose of this note.