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About Some Possible Implementations of the Fractional Calculus

Author

Listed:
  • María Pilar Velasco

    (Department of Applied Mathematics to the Information and Communications Technologies, Universidad Politécnica de Madrid, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • David Usero

    (Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Salvador Jiménez

    (Department of Applied Mathematics to the Information and Communications Technologies, Universidad Politécnica de Madrid, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Luis Vázquez

    (Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • José Luis Vázquez-Poletti

    (Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Mina Mortazavi

    (Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran
    These authors contributed equally to this work.)

Abstract

We present a partial panoramic view of possible contexts and applications of the fractional calculus. In this context, we show some different applications of fractional calculus to different models in ordinary differential equation (ODE) and partial differential equation (PDE) formulations ranging from the basic equations of mechanics to diffusion and Dirac equations.

Suggested Citation

  • María Pilar Velasco & David Usero & Salvador Jiménez & Luis Vázquez & José Luis Vázquez-Poletti & Mina Mortazavi, 2020. "About Some Possible Implementations of the Fractional Calculus," Mathematics, MDPI, vol. 8(6), pages 1-22, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:893-:d:366183
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    References listed on IDEAS

    as
    1. Gao, Xin & Yu, Juebang, 2005. "Chaos in the fractional order periodically forced complex Duffing’s oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1097-1104.
    2. Manuel Duarte Ortigueira & José Tenreiro Machado, 2019. "Fractional Derivatives: The Perspective of System Theory," Mathematics, MDPI, vol. 7(2), pages 1-14, February.
    3. Dumitru Baleanu & Arran Fernandez, 2019. "On Fractional Operators and Their Classifications," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    4. Sheu, Long-Jye & Chen, Hsien-Keng & Chen, Juhn-Horng & Tam, Lap-Mou, 2007. "Chaotic dynamics of the fractionally damped Duffing equation," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1459-1468.
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    Cited by:

    1. Md. Habibur Rahman & Muhammad I. Bhatti & Nicholas Dimakis, 2023. "Employing a Fractional Basis Set to Solve Nonlinear Multidimensional Fractional Differential Equations," Mathematics, MDPI, vol. 11(22), pages 1-15, November.

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