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

Hamid Reza Marzban and Mahtab Manochehri Naeini

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 239, issue C, 223-244

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.

Keywords: Nonlinear delay models; Nonlinear control; Piecewise constant order; Vieta–Fibonacci polynomials; Direct collocation approach (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:239:y:2026:i:c:p:223-244

DOI: 10.1016/j.matcom.2025.05.019

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