Abstract
We point out a major flaw in the so-called conformable calculus. We demonstrate why it fails at defining a fractional order derivative and where exactly these tempting conformability properties come from.
Similar content being viewed by others
References
T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. 279 (2015), 57–66.
A.A. Abdelhakim and J.A.T. Machado, A critical analysis of the conformable derivative. Nonlinear Dynamics (2019), First Online: 02 Jan. 2019, 11 pp.; https://doi.org/10.1007/s11071-018-04741-5.
D.R. Anderson, D.J. Ulness, Properties of the Katugampola fractional derivative with potential application in quantum mechanics. J. Math. Phys. (AIP) 56 (2015), 063502-1–063502-18; DOI: 10.1063/1.4922018.
U.N. Katugampola, A new fractional derivative with classical properties. E-print arXiv:1410.6535 (2014), 8 pp.; Subm. to: Journal of Amer. Math. Society.
R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative. J. Comput. Appl. Math. 264 (2014), 65–70.
F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models. World Scientific, 2010.
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Abdelhakim, A.A. The Flaw in the Conformable Calculus: It is Conformable Because It isNot Fractional. FCAA 22, 242–254 (2019). https://doi.org/10.1515/fca-2019-0016
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1515/fca-2019-0016