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<p>In this work, we propose the utilization of the moving least squares (MLS) approximation for solving time fractional partial integro-differential equations (TFPIDEs) on bounded domains. About the existence and uniqueness of the solution of problem, we used Banach fixed point theorem. To approximate the time Caputo fractional derivative and integral part, we employ a finite difference and trapezoidal method, respectively, with an order of accuracy of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40819_2025_1962_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="90" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {O}(\tau +\tau ^{2-\alpha })\)</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40819_2025_1962_Article_IEq2.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="TEX">\(0&lt;\alpha &lt;1\)</EquationSource> </InlineEquation>. The applicability and validity of this method are thoroughly investigated. Furthermore, we provide an error estimate for evaluating the performance of the proposed approach. Additionally, we solve several numerical problems to validate the accuracy and computational efficiency of our approximation, thus verifying the theoretical analysis.</p>

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The approximate solution of time fractional partial integro-differential equation by moving least squares method

  • 期刊论文

  • 发表日期：

    2025年7月22日

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  • Said Elbostani,
  • Rachid El Jid

摘要

In this work, we propose the utilization of the moving least squares (MLS) approximation for solving time fractional partial integro-differential equations (TFPIDEs) on bounded domains. About the existence and uniqueness of the solution of problem, we used Banach fixed point theorem. To approximate the time Caputo fractional derivative and integral part, we employ a finite difference and trapezoidal method, respectively, with an order of accuracy of \(\mathcal {O}(\tau +\tau ^{2-\alpha })\) , where \(0<\alpha <1\) . The applicability and validity of this method are thoroughly investigated. Furthermore, we provide an error estimate for evaluating the performance of the proposed approach. Additionally, we solve several numerical problems to validate the accuracy and computational efficiency of our approximation, thus verifying the theoretical analysis.