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<p>Based on the topological dual space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {F}_{\theta }^{*}(N^{\prime })\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi mathvariant="script">F</mi> <mrow> <mi>θ</mi> </mrow> <mrow> <mrow /> <mo>∗</mo> </mrow> </msubsup> <mrow> <mo stretchy="false">(</mo> <msup> <mi>N</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> as a space of distributions in infinite-dimensional spaces, we study an analogues of the Airy differential equation, called generalized Airy equation or Airy equation on algebra of generalized functions. We provide a general solution to the generalized Airy equation and prove that this solution is finite-time stochastically stable.</p>

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Airy Equation on Algebra of Generalized Functions

  • 期刊论文

  • 发表日期：

    2026年1月28日

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  • Sultan M. Alzahrani,
  • Afef Ben Farah,
  • Hafedh Rguigui

摘要

Based on the topological dual space \(\mathcal {F}_{\theta }^{*}(N^{\prime })\) F θ ∗ ( N ′ ) as a space of distributions in infinite-dimensional spaces, we study an analogues of the Airy differential equation, called generalized Airy equation or Airy equation on algebra of generalized functions. We provide a general solution to the generalized Airy equation and prove that this solution is finite-time stochastically stable.