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<p>This work investigates the dynamical properties of an initial value problem associated with a conformable spatial <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\texttt{PDE}\)</EquationSource> </InlineEquation> of order <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( \kappa \in (0,1] \)</EquationSource> </InlineEquation> in the specific Lebesgue space <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\( \mathfrak {L}^p_\kappa (\mathbb {R}^+;\mathbb {C}) \)</EquationSource> </InlineEquation>. We first establish that the corresponding solution generates a strongly continuous semigroup. Furthermore, we construct a conjugacy between this semigroup and another defined on the conformable weighted function space <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\( \mathfrak {L}^p_{\rho _\kappa }(\mathbb {R}^+;\mathbb {C}) \)</EquationSource> </InlineEquation>. Under suitable conditions, we show that the system exhibits both hypercyclicity and chaotic behavior.</p>

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On the chaotic behavior of conformable spatial PDEs in specific Lebesgue spaces

  • 期刊论文

  • 发表日期：

    2026年2月16日

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  • Khadija Elkhalloufy,
  • Manal Menchih,
  • Khalid Hilal,
  • Ahmed Kajouni

摘要

This work investigates the dynamical properties of an initial value problem associated with a conformable spatial \(\texttt{PDE}\) of order \( \kappa \in (0,1] \) in the specific Lebesgue space \( \mathfrak {L}^p_\kappa (\mathbb {R}^+;\mathbb {C}) \) . We first establish that the corresponding solution generates a strongly continuous semigroup. Furthermore, we construct a conjugacy between this semigroup and another defined on the conformable weighted function space \( \mathfrak {L}^p_{\rho _\kappa }(\mathbb {R}^+;\mathbb {C}) \) . Under suitable conditions, we show that the system exhibits both hypercyclicity and chaotic behavior.