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Abstract <p>We introduce the reduced Hahn differential transform method (RHDTM). This method can be symbolized as a reduced <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11470_2025_2305_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(q,\omega \)</EquationSource> <!--ComMat2570109Chirko-m1--> </InlineEquation>-differential transform method (R<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11470_2025_2305_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(q,\omega \)</EquationSource> <!--ComMat2570109Chirko-m2--> </InlineEquation>DTM). We construct the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11470_2025_2305_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(q,\omega \)</EquationSource> <!--ComMat2570109Chirko-m3--> </InlineEquation>-analogs of some problems, each including a non-linear partial differential equation, Burgers’ equation, and a partial-integro-differential equation, and then solve them by applying the RHDTM. Additionally, we explain the advantages of the presented method in these problems.</p>

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Reduced Hahn Differential Transform Method

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • M. A. Chirko,
  • F. Hıra

摘要

Abstract

We introduce the reduced Hahn differential transform method (RHDTM). This method can be symbolized as a reduced \(q,\omega \) -differential transform method (R \(q,\omega \) DTM). We construct the \(q,\omega \) -analogs of some problems, each including a non-linear partial differential equation, Burgers’ equation, and a partial-integro-differential equation, and then solve them by applying the RHDTM. Additionally, we explain the advantages of the presented method in these problems.