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A New Look at the Initial Condition Problem

Author

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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)

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.

Suggested Citation

  • Manuel D. Ortigueira, 2022. "A New Look at the Initial Condition Problem," Mathematics, MDPI, vol. 10(10), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1771-:d:821719
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    References listed on IDEAS

    as
    1. Duarte Valério & Manuel D. Ortigueira & António M. Lopes, 2022. "How Many Fractional Derivatives Are There?," Mathematics, MDPI, vol. 10(5), pages 1-18, February.
    2. Boularouk, Y. & Djeddour, K., 2015. "New approximation for ARMA parameters estimate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 116-122.
    3. Manuel Duarte Ortigueira & José Tenreiro Machado, 2020. "Revisiting the 1D and 2D Laplace Transforms," Mathematics, MDPI, vol. 8(8), pages 1-24, August.
    4. Edmundo Capelas de Oliveira & José António Tenreiro Machado, 2014. "A Review of Definitions for Fractional Derivatives and Integral," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-6, June.
    5. P. Brockwell, 2014. "Recent results in the theory and applications of CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 647-685, August.
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    Cited by:

    1. Yuri Luchko, 2023. "Fractional Integrals and Derivatives: “True” versus “False”," Mathematics, MDPI, vol. 11(13), pages 1-2, July.

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