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Existence and Hyers–Ulam Stability for Random Impulsive Stochastic Pantograph Equations with the Caputo Fractional Derivative

Author

Listed:
  • Dongdong Gao

    (Department of Mathematics and Computer Science, Tongling University, Tongling 244000, China)

  • Jianli Li

    (College of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China)

Abstract

In this paper, we study the existence, uniqueness and Hyers–Ulam stability of a class of fractional stochastic pantograph equations with random impulses. Firstly, we establish sufficient conditions to ensure the existence of solutions for the considered equations by applying Schaefer’s fixed point theorem under relaxed linear growth conditions. Secondly, we prove the solution for the considered equations is Hyers–Ulam stable via Gronwall’s inequality. Moreover, the previous literature will be significantly generalized in our paper. Finally, an example is given to explain the efficiency of the obtained results.

Suggested Citation

  • Dongdong Gao & Jianli Li, 2024. "Existence and Hyers–Ulam Stability for Random Impulsive Stochastic Pantograph Equations with the Caputo Fractional Derivative," Mathematics, MDPI, vol. 12(8), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1145-:d:1373480
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    References listed on IDEAS

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    1. Mao, Wei & Hu, Liangjian & Mao, Xuerong, 2015. "The existence and asymptotic estimations of solutions to stochastic pantograph equations with diffusion and Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 883-896.
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