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On development of fractional calculus during the last fifty years

Author

Listed:
  • J. A. Tenreiro Machado

    (Institute of Engineering, Polytechnic of Porto)

  • Alexandra M. S. F. Galhano

    (Institute of Engineering, Polytechnic of Porto)

  • Juan J. Trujillo

    (Universidad de La Laguna)

Abstract

Fractional calculus generalizes integer order derivatives and integrals. During the last half century a considerable progress took place in this scientific area. This paper addresses the evolution and establishes an assertive measure of the research development.

Suggested Citation

  • J. A. Tenreiro Machado & Alexandra M. S. F. Galhano & Juan J. Trujillo, 2014. "On development of fractional calculus during the last fifty years," Scientometrics, Springer;Akadémiai Kiadó, vol. 98(1), pages 577-582, January.
    • Handle: RePEc:spr:scient:v:98:y:2014:i:1:d:10.1007_s11192-013-1032-6
    DOI: 10.1007/s11192-013-1032-6
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    References listed on IDEAS

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    1. Samuel Arbesman, 2011. "Quantifying the ease of scientific discovery," Scientometrics, Springer;Akadémiai Kiadó, vol. 86(2), pages 245-250, February.
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    Cited by:

    1. Vellasco-Gomes, Arianne & de Figueiredo Camargo, Rubens & Bruno-Alfonso, Alexys, 2020. "Energy bands and Wannier functions of the fractional Kronig-Penney model," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    2. Zaheer Masood & Muhammad Asif Zahoor Raja & Naveed Ishtiaq Chaudhary & Khalid Mehmood Cheema & Ahmad H. Milyani, 2021. "Fractional Dynamics of Stuxnet Virus Propagation in Industrial Control Systems," Mathematics, MDPI, vol. 9(17), pages 1-27, September.
    3. Vasily E. Tarasov, 2019. "Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models," Mathematics, MDPI, vol. 7(6), pages 1-50, June.
    4. Vasily E. Tarasov, 2024. "Exact Finite-Difference Calculus: Beyond Set of Entire Functions," Mathematics, MDPI, vol. 12(7), pages 1-37, March.
    5. Gauhar Rahman & Kottakkaran Sooppy Nisar & Thabet Abdeljawad, 2020. "Tempered Fractional Integral Inequalities for Convex Functions," Mathematics, MDPI, vol. 8(4), pages 1-12, April.
    6. Vasily E. Tarasov, 2021. "Integral Equations of Non-Integer Orders and Discrete Maps with Memory," Mathematics, MDPI, vol. 9(11), pages 1-12, May.
    7. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    8. Tarasov, Vasily E., 2020. "Fractional econophysics: Market price dynamics with memory effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    9. Vasily E. Tarasov, 2022. "General Non-Local Continuum Mechanics: Derivation of Balance Equations," Mathematics, MDPI, vol. 10(9), pages 1-43, April.
    10. Kottakkaran Sooppy Nisar, 2019. "Fractional Integrations of a Generalized Mittag-Leffler Type Function and Its Application," Mathematics, MDPI, vol. 7(12), pages 1-13, December.

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