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<p>In this paper, we study a variational calculus with the truncated <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40819_2025_1984_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {V}\)</EquationSource> </InlineEquation>-fractional derivatives. We derive the necessary optimality conditions by formulating the corresponding Euler-Lagrange equations and prove their validity. Some illustrative applications are presented. Through these applications we have seen the effect of the <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40819_2025_1984_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> </InlineEquation>-parameter on the obtained solutions.</p>

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Truncated \(\mathcal {V}\)-Fractional Derivative and Variational Problems

  • 期刊论文

  • 发表日期：

    2025年7月29日

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  • Brahim El Ansari,
  • El Hassan El Kinani,
  • Abdelaziz Ouhadan

摘要

In this paper, we study a variational calculus with the truncated \(\mathcal {V}\) -fractional derivatives. We derive the necessary optimality conditions by formulating the corresponding Euler-Lagrange equations and prove their validity. Some illustrative applications are presented. Through these applications we have seen the effect of the \(\alpha \) -parameter on the obtained solutions.