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<p>This study presents semi-analytical solutions for the fractional Fornberg–Whitham (FFW) equation using the Fractional Temimi–Ansari Method (FTAM). Fractional derivatives are defined in the senses of Atangana–Baleanu–Caputo (ABC) and Caputo. The existence and uniqueness of solutions are rigorously examined. Furthermore, a detailed discussion of the FTAM framework, including convergence analysis is provided. The accuracy of the obtained solutions is validated through comparisons with exact solutions when the fractional order is <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mu =1\)</EquationSource> </InlineEquation>. Another key objective of the study is to compare the two fractional derivative definitions to assess the extent to which each captures memory effects from the past. Owing to its Mittag-Leffler-type kernel, the ABC derivative enhances memory effects and promotes faster stabilization.</p>

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Semi analytical solution strategy for fractional Fornberg Whitham equation using Temimi Ansari method

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  • 发表日期：

    2025年11月28日

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  • Anas A. M. Arafa,
  • Essam M. Elsaid,
  • Sameh E. Ahmed,
  • Sameh A. Hussein,
  • A. A. Al Qarni,
  • Mohamed R. Eid

摘要

This study presents semi-analytical solutions for the fractional Fornberg–Whitham (FFW) equation using the Fractional Temimi–Ansari Method (FTAM). Fractional derivatives are defined in the senses of Atangana–Baleanu–Caputo (ABC) and Caputo. The existence and uniqueness of solutions are rigorously examined. Furthermore, a detailed discussion of the FTAM framework, including convergence analysis is provided. The accuracy of the obtained solutions is validated through comparisons with exact solutions when the fractional order is \(\mu =1\) . Another key objective of the study is to compare the two fractional derivative definitions to assess the extent to which each captures memory effects from the past. Owing to its Mittag-Leffler-type kernel, the ABC derivative enhances memory effects and promotes faster stabilization.