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<p>The objective of this work is to present a new direct numerical method to solve fractional optimal control problems (FOCPs) based on the Vieta-Lucas (V-L) polynomials. V-L polynomials are a type of weighted orthogonal polynomials that can be effectively employed to address a variety of natural and engineered problems. The fractional derivative is addressed in the Caputo sense. The approximate solution of three types of FOCPs can be obtained by using the operational matrices of shifted (V-L) polynomials, the Gauss-Legendre quadrature method, and optimization techniques. The key and efficient feature of the proposed method is its ability to transform the problem at hand into a system of algebraic equations, which significantly reduces computational costs and CPU time. Moreover, the error of the performance index achieved by the computational approach is investigated. To demonstrate the feasibility and effectiveness of the mentioned method in addressing FOCPs, several numerical experiments have been conducted. Furthermore, Example 8&#xa0;presents a practical illustration of a cancer model.</p>

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A Numerical Schemes Based on Vieta-Lucas Polynomials for Evaluating the Approximate Solution of Some Types of Fractional Optimal Control Problems

  • 期刊论文

  • 发表日期：

    2025年3月3日

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  • Marzieh Pourbabaee,
  • Abbas Saadatmandi

摘要

The objective of this work is to present a new direct numerical method to solve fractional optimal control problems (FOCPs) based on the Vieta-Lucas (V-L) polynomials. V-L polynomials are a type of weighted orthogonal polynomials that can be effectively employed to address a variety of natural and engineered problems. The fractional derivative is addressed in the Caputo sense. The approximate solution of three types of FOCPs can be obtained by using the operational matrices of shifted (V-L) polynomials, the Gauss-Legendre quadrature method, and optimization techniques. The key and efficient feature of the proposed method is its ability to transform the problem at hand into a system of algebraic equations, which significantly reduces computational costs and CPU time. Moreover, the error of the performance index achieved by the computational approach is investigated. To demonstrate the feasibility and effectiveness of the mentioned method in addressing FOCPs, several numerical experiments have been conducted. Furthermore, Example 8 presents a practical illustration of a cancer model.