Variable-Order Fractional Scale Calculus

Duarte Valério () and Manuel D. Ortigueira
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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

Mathematics, 2023, vol. 11, issue 21, 1-13

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.

Keywords: scale derivative; Hadamard derivative; variable-order derivative; logarithmic series (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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