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Integral Equations of Non-Integer Orders and Discrete Maps with Memory

Author

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  • Vasily E. Tarasov

    (Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
    Faculty “Information Technologies and Applied Mathematics”, Moscow Aviation Institute, National Research University, 125993 Moscow, Russia)

Abstract

In this paper, we use integral equations of non-integer orders to derive discrete maps with memory. Note that discrete maps with memory were not previously derived from fractional integral equations of non-integer orders. Such a derivation of discrete maps with memory is proposed for the first time in this work. In this paper, we derived discrete maps with nonlocality in time and memory from exact solutions of fractional integral equations with the Riemann–Liouville and Hadamard type fractional integrals of non-integer orders and periodic sequence of kicks that are described by Dirac delta-functions. The suggested discrete maps with nonlocality in time are derived from these fractional integral equations without any approximation and can be considered as exact discrete analogs of these equations. The discrete maps with memory, which are derived from integral equations with the Hadamard type fractional integrals, do not depend on the period of kicks.

Suggested Citation

  • Vasily E. Tarasov, 2021. "Integral Equations of Non-Integer Orders and Discrete Maps with Memory," Mathematics, MDPI, vol. 9(11), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1177-:d:560594
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    References listed on IDEAS

    as
    1. Tarasova, Valentina V. & Tarasov, Vasily E., 2017. "Logistic map with memory from economic model," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 84-91.
    2. 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.
    3. Vasily E. Tarasov, 2020. "Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 8(5), pages 1-3, April.
    4. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Logistic map with memory from economic model," Papers 1712.09092, arXiv.org.
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    Cited by:

    1. Vasily E. Tarasov, 2021. "General Fractional Dynamics," Mathematics, MDPI, vol. 9(13), pages 1-26, June.
    2. Méndez-Bermúdez, J.A. & Peralta-Martinez, Kevin & Sigarreta, José M. & Leonel, Edson D., 2023. "Leaking from the phase space of the Riemann–Liouville fractional standard map," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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