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<p>This paper investigates the existence, uniqueness, and stability of solutions to fractional stochastic differential systems driven by non-Gaussian processes and Poisson jumps. The existence of solutions is established via Krasnoselskii’s fixed-point theorem, whereas uniqueness is obtained through Banach’s fixed-point theorem. Furthermore, several stability concepts are examined, including Hyers–Ulam stability, Hyers–Ulam–Rassias stability, and generalized Hyers–Ulam–Rassias stability. To support the theoretical results, three illustrative examples are provided, demonstrating the applicability of the proposed framework. Graphical interpretations generated through MATLAB further visualize the solution behavior under various conditions. By combining analytical and numerical methods, this study improves our understanding of fractional stochastic systems overall and highlights how stochastic effects and fractional dynamics influence system behavior.</p>

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Existence, uniqueness, and stability of fractional stochastic differential equations driven by non-Gaussian processes and Poisson jumps

  • 期刊论文

  • 发表日期：

    2026年6月15日

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  • Rahim Shah,
  • Earige Tanveer

摘要

This paper investigates the existence, uniqueness, and stability of solutions to fractional stochastic differential systems driven by non-Gaussian processes and Poisson jumps. The existence of solutions is established via Krasnoselskii’s fixed-point theorem, whereas uniqueness is obtained through Banach’s fixed-point theorem. Furthermore, several stability concepts are examined, including Hyers–Ulam stability, Hyers–Ulam–Rassias stability, and generalized Hyers–Ulam–Rassias stability. To support the theoretical results, three illustrative examples are provided, demonstrating the applicability of the proposed framework. Graphical interpretations generated through MATLAB further visualize the solution behavior under various conditions. By combining analytical and numerical methods, this study improves our understanding of fractional stochastic systems overall and highlights how stochastic effects and fractional dynamics influence system behavior.