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<p>In this study, we investigated stochastic mixed Voltera - Fredholm type nonlinear third-order dispersion equation within Hilbert spaces. Initially, we establish the existence of mild solutions to the equation by applying Schauder’s fixed point theorem, properties of infinite-dimensional semigroups, and methods from stochastic analysis. Subsequently, we derive a novel set of sufficient conditions that ensure the Approximate Controllability of the primary system. To demonstrate the practical use of the main result, an example is presented.</p>

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Existence of Mild Solutions and Approximate Controllability of Stochastic Mixed Voltera - Fredholm Type Nonlinear Third-order Dispersion Equation

  • 期刊论文

  • 发表日期：

    2025年10月21日

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  • Avanish Shukla,
  • Rohit Patel,
  • Naveen Kumar

摘要

In this study, we investigated stochastic mixed Voltera - Fredholm type nonlinear third-order dispersion equation within Hilbert spaces. Initially, we establish the existence of mild solutions to the equation by applying Schauder’s fixed point theorem, properties of infinite-dimensional semigroups, and methods from stochastic analysis. Subsequently, we derive a novel set of sufficient conditions that ensure the Approximate Controllability of the primary system. To demonstrate the practical use of the main result, an example is presented.