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<p>In this paper, we employ the Banach fixed-point Theorem to establish the existence and the uniqueness of a solution for a <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1668_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>-Riemann-Liouville fractional stochastic differential equation. Moreover, we prove some properties of the energy growth bound and the asymptotic behavior of the random solution. Examples are provided to illustrate the validity of our results.</p>

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Existence and Uniqueness of Solution for a \(\psi \)-Riemann-Liouville Fractional Stochastic Differential Equation

  • 期刊论文

  • 发表日期：

    2025年2月22日

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  • Walid Hammami,
  • Samah Horrigue,
  • Soufiane Gasmi

摘要

In this paper, we employ the Banach fixed-point Theorem to establish the existence and the uniqueness of a solution for a \(\psi \) ψ -Riemann-Liouville fractional stochastic differential equation. Moreover, we prove some properties of the energy growth bound and the asymptotic behavior of the random solution. Examples are provided to illustrate the validity of our results.