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<p>We study the Müntz–Legendre wavelet collocation method for solving optimal control problems with constraints as the fractional differential equations equipped with load points, called fractional-loaded optimal control problems. An indirect method has been used for the solution of the proposed problem, and thus, the necessary as well as sufficient optimality conditions are derived for the fractional-loaded optimal control problem by using the method of calculus of variations and integration by parts formula. The left and right operational matrices of integration have been utilized to transform the necessary optimality conditions into a system of algebraic equations using the collocation method and convergence of the method is proved. Finally, test problems have been taken to verify the convergence of the proposed method to the true solution via the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42979_2025_3997_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-errors in approximation.</p>

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Müntz–Legendre Wavelet Collocation Method for the Solution of Optimal Control Problems with Fractional-Loaded Differential Equations

  • 期刊论文

  • 发表日期：

    2025年5月12日

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  • Ritu Kumari,
  • Mani Mehra

摘要

We study the Müntz–Legendre wavelet collocation method for solving optimal control problems with constraints as the fractional differential equations equipped with load points, called fractional-loaded optimal control problems. An indirect method has been used for the solution of the proposed problem, and thus, the necessary as well as sufficient optimality conditions are derived for the fractional-loaded optimal control problem by using the method of calculus of variations and integration by parts formula. The left and right operational matrices of integration have been utilized to transform the necessary optimality conditions into a system of algebraic equations using the collocation method and convergence of the method is proved. Finally, test problems have been taken to verify the convergence of the proposed method to the true solution via the \(L_2\) L 2 -errors in approximation.