A New Look at the Initial Condition Problem

Manuel D. Ortigueira
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Manuel D. Ortigueira: Centre of Technology and Systems—UNINOVA and Department of Electrical Engineering, NOVA School of Science and Technology of NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, Portugal

Mathematics, 2022, vol. 10, issue 10, 1-17

Abstract: In this paper, some myths associated to the initial condition problem are studied and demystified. It is shown that the initial conditions provided by the one-sided Laplace transform are not those required for Riemann-Liouville and Caputo derivatives. The problem is studied and solved with generality as well as applied to continuous-time fractional autoregressive-moving average systems.

Keywords: initial conditions; fractional derivative; linear systems; Riemann-Liouville derivative; Caputo derivative; FARMA (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:10:p:1771-:d:821719

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