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<p>This work extends the multistep Chebyshev spectral method to obtain approximate solutions of fractional pantograph differential equations. The fractional derivative is applied in the Caputo sense. We first establish the existence and uniqueness of the solutions under reasonable assumptions regarding nonlinearity. Next, we analyze the error estimate of the proposed numerical scheme under the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2852_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="35" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^{2}-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>norm. Finally, numerical experiments are conducted to validate our theoretical analysis.</p>

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A Multistep Chebyshev Collocation Scheme for Fractional Differential Equations of Pantograph Type

  • 期刊论文

  • 发表日期：

    2025年5月7日

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  • Changqing Yang,
  • Jianhua Hou,
  • Xiaoguang Lv

摘要

This work extends the multistep Chebyshev spectral method to obtain approximate solutions of fractional pantograph differential equations. The fractional derivative is applied in the Caputo sense. We first establish the existence and uniqueness of the solutions under reasonable assumptions regarding nonlinearity. Next, we analyze the error estimate of the proposed numerical scheme under the \(L^{2}-\) L 2 - norm. Finally, numerical experiments are conducted to validate our theoretical analysis.