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<p>This research introduces a novel mathematical model for brain tumor growth incorporating a fractal fractional derivative. We investigate the existence and uniqueness of solutions for this model, as well as its stability properties, using a novel contraction known as the generalized <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3276_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>α</mi> <mo>−</mo> <mi>ψ</mi> </math></EquationSource> <EquationSource Format="TEX">$\alpha -\psi $</EquationSource> </InlineEquation>-Geraghty-type contraction. Our stability analysis is based on the Ulam–Hyers framework. The findings presented in this study constitute a significant contribution to the field.</p>

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Existence, stability, and numerical simulation of a nonlinear brain tumor model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月23日

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  • Hojjat Afshari,
  • Sabileh Kalantari,
  • Mehrdad Anvari,
  • H. R. Marasi

摘要

This research introduces a novel mathematical model for brain tumor growth incorporating a fractal fractional derivative. We investigate the existence and uniqueness of solutions for this model, as well as its stability properties, using a novel contraction known as the generalized α − ψ $\alpha -\psi $ -Geraghty-type contraction. Our stability analysis is based on the Ulam–Hyers framework. The findings presented in this study constitute a significant contribution to the field.