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<p>This study examines the dynamics of bacterial chemotaxis in <i>Escherichia coli</i> by formulating a one-dimensional hyperbolic model enhanced with conformable fractional derivatives. These derivatives effectively capture memory effects and nonlocal interactions, providing a more comprehensive representation of bacterial movement. Utilizing the two-variable <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2424_Article_IEq1.gif" Format="GIF" Height="33" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left( \frac{G^\prime }{G}, \frac{1}{G}\right)\)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mfrac> <msup> <mi>G</mi> <mo>′</mo> </msup> <mi>G</mi> </mfrac> <mo>,</mo> <mfrac> <mn>1</mn> <mi>G</mi> </mfrac> </mfenced> </math></EquationSource> </InlineEquation> expansion method, we derive analytical solutions, encompassing hyperbolic, trigonometric, and rational function forms. These solutions reveal distinct wave phenomena, including bell-shaped solitary waves, singular solitons, and kink-type waves. The fractional-order model bridges subdiffusive and superdiffusive dynamics, offering a versatile framework for investigating chemotactic responses in complex environments. This work advances theoretical understanding of microbial migration and highlights the utility of fractional-order partial differential equations in capturing the intricate, memory-driven dynamics of biological systems.</p>

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Traveling wave solutions for a fractional-order hyperbolic model of chemotaxis in Escherichia coli

  • 期刊论文

  • 发表日期：

    2025年5月27日

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  • N. Annapoorani,
  • N. Keerthana,
  • Kottakkaran Sooppy Nisar

摘要

This study examines the dynamics of bacterial chemotaxis in Escherichia coli by formulating a one-dimensional hyperbolic model enhanced with conformable fractional derivatives. These derivatives effectively capture memory effects and nonlocal interactions, providing a more comprehensive representation of bacterial movement. Utilizing the two-variable \(\left( \frac{G^\prime }{G}, \frac{1}{G}\right)\) G ′ G , 1 G expansion method, we derive analytical solutions, encompassing hyperbolic, trigonometric, and rational function forms. These solutions reveal distinct wave phenomena, including bell-shaped solitary waves, singular solitons, and kink-type waves. The fractional-order model bridges subdiffusive and superdiffusive dynamics, offering a versatile framework for investigating chemotactic responses in complex environments. This work advances theoretical understanding of microbial migration and highlights the utility of fractional-order partial differential equations in capturing the intricate, memory-driven dynamics of biological systems.