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Power Functions and Their Relationship with the Unified Fractional Derivative

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  • Manuel Duarte Ortigueira

    (CTS-UNINOVA and LASI, NOVA School of Science and Technology, NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, Portugal)

Abstract

The different forms of power functions will be studied in connection with the unified fractional derivative, and their Fourier transform will be computed. In particular, one-sided, even, and odd powers will be studied.

Suggested Citation

  • Manuel Duarte Ortigueira, 2025. "Power Functions and Their Relationship with the Unified Fractional Derivative," Mathematics, MDPI, vol. 13(5), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:852-:d:1605315
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    References listed on IDEAS

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    1. 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.
    2. Duarte Valério & Manuel D. Ortigueira, 2023. "Variable-Order Fractional Scale Calculus," Mathematics, MDPI, vol. 11(21), pages 1-13, November.
    3. Manuel Duarte Ortigueira & José Tenreiro Machado, 2019. "Fractional Derivatives: The Perspective of System Theory," Mathematics, MDPI, vol. 7(2), pages 1-14, February.
    4. 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.
    5. Vasily E. Tarasov, 2023. "Multi-Kernel General Fractional Calculus of Arbitrary Order," Mathematics, MDPI, vol. 11(7), pages 1-32, April.
    6. Juan Luis González-Santander & Francesco Mainardi, 2024. "Some Fractional Integral and Derivative Formulas Revisited," Mathematics, MDPI, vol. 12(17), pages 1-13, September.
    7. Manuel Duarte Ortigueira, 2006. "Riesz potential operators and inverses via fractional centred derivatives," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-12, August.
    Full references (including those not matched with items on IDEAS)

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