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Desiderata for Fractional Derivatives and Integrals

Author

Listed:
  • Rudolf Hilfer

    (ICP, Fakultät für Mathematik und Physik, Universität Stuttgart, Allmandring 3, 70569 Stuttgart, Germany)

  • Yuri Luchko

    (Fachbereich Mathematik-Physik-Chemie, Beuth Hochschule für Technik Berlin, Luxemburger Str. 10, 13353 Berlin, Germany)

Abstract

The purpose of this brief article is to initiate discussions in this special issue by proposing desiderata for calling an operator a fractional derivative or a fractional integral. Our desiderata are neither axioms nor do they define fractional derivatives or integrals uniquely. Instead they intend to stimulate the field by providing guidelines based on a small number of time honoured and well established criteria.

Suggested Citation

  • Rudolf Hilfer & Yuri Luchko, 2019. "Desiderata for Fractional Derivatives and Integrals," Mathematics, MDPI, vol. 7(2), pages 1-5, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:149-:d:203523
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    Citations

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    Cited by:

    1. Vasily E. Tarasov, 2023. "General Fractional Calculus in Multi-Dimensional Space: Riesz Form," Mathematics, MDPI, vol. 11(7), pages 1-20, March.
    2. Vasily E. Tarasov, 2020. "Non-Linear Macroeconomic Models of Growth with Memory," Mathematics, MDPI, vol. 8(11), pages 1-22, November.
    3. Yuri Luchko, 2022. "Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense," Mathematics, MDPI, vol. 10(6), pages 1-24, March.
    4. Isah, Sunday Simon & Fernandez, Arran & Özarslan, Mehmet Ali, 2023. "On bivariate fractional calculus with general univariate analytic kernels," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    5. Shiri, Babak & Baleanu, Dumitru, 2023. "All linear fractional derivatives with power functions’ convolution kernel and interpolation properties," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    6. Daniel Cao Labora, 2020. "Fractional Integral Equations Tell Us How to Impose Initial Values in Fractional Differential Equations," Mathematics, MDPI, vol. 8(7), pages 1-17, July.
    7. Christopher Nicholas Angstmann & Byron Alexander Jacobs & Bruce Ian Henry & Zhuang Xu, 2020. "Intrinsic Discontinuities in Solutions of Evolution Equations Involving Fractional Caputo–Fabrizio and Atangana–Baleanu Operators," Mathematics, MDPI, vol. 8(11), pages 1-16, November.
    8. Mohammed Al-Refai & Yuri Luchko, 2023. "The General Fractional Integrals and Derivatives on a Finite Interval," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    9. Vasily E. Tarasov & Svetlana S. Tarasova, 2020. "Fractional Derivatives and Integrals: What Are They Needed For?," Mathematics, MDPI, vol. 8(2), pages 1-22, January.
    10. Oscar Martínez-Fuentes & Fidel Meléndez-Vázquez & Guillermo Fernández-Anaya & José Francisco Gómez-Aguilar, 2021. "Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities," Mathematics, MDPI, vol. 9(17), pages 1-29, August.

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