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<p>This paper investigates the stochastic dynamics of a fractional-order Leslie-Gower eco-epidemiological model under white noise perturbations. The fractional derivatives are interpreted in the Caputo sense, and the stochastic fractional differential equations are formulated in integral form, with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(dt^{\alpha }\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <msup> <mi>t</mi> <mi>α</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> denoting the fractional-order time increment. We prove the existence and uniqueness of global positive solutions and establish sufficient conditions for stochastic boundedness, extinction, and mean persistence using stochastic Lyapunov functionals, a fractional Itô formula, and comparison theorems. The stochastic stability of equilibrium points is analyzed, revealing noise-induced shifts between deterministic and stochastic dynamical regimes, including stochastic stabilization. An extended Euler-Maruyama scheme is developed for numerical simulation, and the results illustrate complex phenomena, such as noise-induced stabilization and stochastic bifurcations. Our findings highlight the interplay between environmental randomness and fractional memory in ecological systems. To the best of our knowledge, this work provides a systematic analytical and numerical framework for fractional-order stochastic Leslie-Gower systems under white noise.</p>

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Long-term dynamics of a fractional Leslie-Gower system with environmental stochasticity

  • 期刊论文

  • 发表日期：

    2026年7月19日

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  • Mona Bin-Asfour,
  • Ghaliah Alhamzi,
  • Najat Almutairi,
  • Faisal Muteb K. Almalki,
  • Abdullah A. Alahmari,
  • Sayed Saber

摘要

This paper investigates the stochastic dynamics of a fractional-order Leslie-Gower eco-epidemiological model under white noise perturbations. The fractional derivatives are interpreted in the Caputo sense, and the stochastic fractional differential equations are formulated in integral form, with \(dt^{\alpha }\) d t α denoting the fractional-order time increment. We prove the existence and uniqueness of global positive solutions and establish sufficient conditions for stochastic boundedness, extinction, and mean persistence using stochastic Lyapunov functionals, a fractional Itô formula, and comparison theorems. The stochastic stability of equilibrium points is analyzed, revealing noise-induced shifts between deterministic and stochastic dynamical regimes, including stochastic stabilization. An extended Euler-Maruyama scheme is developed for numerical simulation, and the results illustrate complex phenomena, such as noise-induced stabilization and stochastic bifurcations. Our findings highlight the interplay between environmental randomness and fractional memory in ecological systems. To the best of our knowledge, this work provides a systematic analytical and numerical framework for fractional-order stochastic Leslie-Gower systems under white noise.