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<p>We discuss the existence, uniqueness, trajectory (T)-controllability, and Ulam-Hyer’s stability of solutions for a coupled non-linear fractional order stochastic differential systems (FSDEs) with integral boundary conditions (IBC) via fixed point approach namely Banach fixed point theorem. The mild solution of the coupled system is obtained via Green’s functions. We obtain some relaxed conditions for the existence and uniqueness of the mentioned problem. Further, we develop some conditions for Ulam-Hyer’s stability (UHS) for the non-linear fractional order coupled systems. Moreover, we demonstrate the main results through the concept of T-controllability for a coupled FSDEs via the Gronwall’s inequality. To demonstrate our main result, we provide a proper example.</p>

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Stability and T-Controllability for a Coupled Fractional Stochastic Integro Systems with Integral Boundary Conditions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月4日

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  • Dhanalakshmi Kasinathan,
  • Dimplekumar Chalishajar,
  • Ramkumar Kasinathan,
  • Ravikumar Kasinathan

摘要

We discuss the existence, uniqueness, trajectory (T)-controllability, and Ulam-Hyer’s stability of solutions for a coupled non-linear fractional order stochastic differential systems (FSDEs) with integral boundary conditions (IBC) via fixed point approach namely Banach fixed point theorem. The mild solution of the coupled system is obtained via Green’s functions. We obtain some relaxed conditions for the existence and uniqueness of the mentioned problem. Further, we develop some conditions for Ulam-Hyer’s stability (UHS) for the non-linear fractional order coupled systems. Moreover, we demonstrate the main results through the concept of T-controllability for a coupled FSDEs via the Gronwall’s inequality. To demonstrate our main result, we provide a proper example.