Skip to main content
Log in

The Flaw in the Conformable Calculus: It is Conformable Because It isNot Fractional

  • Discussion Paper
  • Published:
Fractional Calculus and Applied Analysis Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. 279 (2015), 57–66.

    Article  MathSciNet  Google Scholar 

  2. 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.

    Google Scholar 

  3. 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.

  4. 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.

    Google Scholar 

  5. R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative. J. Comput. Appl. Math. 264 (2014), 65–70.

    Article  MathSciNet  Google Scholar 

  6. F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models. World Scientific, 2010.

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ahmed A. Abdelhakim.

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1515/fca-2019-0016

Keywords

Key Words and Phrases

Navigation