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An innovative class of orthogonal functions based on the fractional Vieta–Fibonacci functions and its utilization in optimal control of piecewise constant order systems consisting of delay

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  • Marzban, Hamid Reza
  • Manochehri Naeini, Mahtab

Abstract

An essential category of fractional piecewise constant order control systems involving delay is studied. As far as we know, these vital models of systems have not been discussed in the literature. The devised approach is based upon a modification and generalization of the fractional Vieta–Fibonacci polynomials. An efficient integral operator is acquired and novel theoretical consequences related to the presented fractional basis are provided. The exactness and capability of the devised approach are justified by illustrating five challenging test problems. The simulation outputs verify the effectiveness of the devised basis.

Suggested Citation

  • Marzban, Hamid Reza & Manochehri Naeini, Mahtab, 2026. "An innovative class of orthogonal functions based on the fractional Vieta–Fibonacci functions and its utilization in optimal control of piecewise constant order systems consisting of delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 223-244.
    • Handle: RePEc:eee:matcom:v:239:y:2026:i:c:p:223-244
    DOI: 10.1016/j.matcom.2025.05.019
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    References listed on IDEAS

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