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<p>This paper examines the asymptotic behavior of solutions to linear fractal differential equations within the framework of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( F^\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>F</mi> <mi>α</mi> </msup> </math></EquationSource> </InlineEquation>-calculus. We identify the conditions that determine whether the solutions remain stable, grow, or decay. These dynamics are further explored through comprehensive examples and theoretical findings, emphasizing the self-similar characteristics of solutions, including first- and second-order higher <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-order fractal differential equations.</p>

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Asymptotic Behavior of Solutions to Linear Fractal Differential Equations

  • 期刊论文

  • 发表日期：

    2026年3月19日

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  • Alireza Khalili Golmankhaneh,
  • Cemil Tunç,
  • Hamdullah Şevli

摘要

This paper examines the asymptotic behavior of solutions to linear fractal differential equations within the framework of \( F^\alpha \) F α -calculus. We identify the conditions that determine whether the solutions remain stable, grow, or decay. These dynamics are further explored through comprehensive examples and theoretical findings, emphasizing the self-similar characteristics of solutions, including first- and second-order higher \(\alpha \) α -order fractal differential equations.