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Variable-Order Fractional Scale Calculus

Author

Listed:
  • Duarte Valério

    (IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal)

  • Manuel D. Ortigueira

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

Abstract

General variable-order fractional scale derivatives are introduced and studied. Both the stretching and the shrinking cases are considered for definitions of the derivatives of the GL type and of the Hadamard type. Their properties are deduced and discussed. Fractional variable-order systems of autoregressive–moving-average type are introduced and exemplified. The corresponding transfer functions are obtained and used to find the corresponding impulse responses.

Suggested Citation

  • Duarte Valério & Manuel D. Ortigueira, 2023. "Variable-Order Fractional Scale Calculus," Mathematics, MDPI, vol. 11(21), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4549-:d:1274178
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    References listed on IDEAS

    as
    1. Bertram Ross & Stefan Samko, 1995. "Fractional integration operator of variable order in the holder spaces H λ ( x )," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 18, pages 1-12, January.
    2. Almeida, Ricardo & Torres, Delfim F.M., 2015. "Computing Hadamard type operators of variable fractional order," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 74-88.
    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. Dominik Sierociuk & Wiktor Malesza, 2017. "Fractional variable order discrete-time systems, their solutions and properties," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(14), pages 3098-3105, October.
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