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Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays

Author

Listed:
  • R. Sakthivel
  • P. Revathi
  • N. I. Mahmudov

Abstract

We study the existence and asymptotic stability in p th moment of a mild solution to a class of nonlinear fractional neutral stochastic differential equations with infinite delays in Hilbert spaces. A set of novel sufficient conditions are derived with the help of semigroup theory and fixed point technique for achieving the required result. The uniqueness of the solution of the considered problem is also studied under suitable conditions. Finally, an example is given to illustrate the obtained theory.

Suggested Citation

  • R. Sakthivel & P. Revathi & N. I. Mahmudov, 2013. "Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, February.
    • Handle: RePEc:hin:jnlaaa:769257
    DOI: 10.1155/2013/769257
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    Cited by:

    1. Tianxiang Yao & Xianghong Lai, 2014. "Mean‐Square Exponential Stability Analysis of Stochastic Neural Networks with Time‐Varying Delays via Fixed Point Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. Wang, Bingjun & Yuan, Mingxia, 2019. "Forward-backward stochastic differential equations driven by G-Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 39-47.
    3. Hai Zhang & Daiyong Wu & Jinde Cao, 2014. "Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Yiheng Wei & Hamid Reza Karimi & Shu Liang & Qing Gao & Yong Wang, 2014. "General Output Feedback Stabilization for Fractional Order Systems: An LMI Approach," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Ren, Yong & He, Qian & Gu, Yuanfang & Sakthivel, R., 2018. "Mean-square stability of delayed stochastic neural networks with impulsive effects driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 56-66.
    6. Singh, Ajeet & Shukla, Anurag & Vijayakumar, V. & Udhayakumar, R., 2021. "Asymptotic stability of fractional order (1,2] stochastic delay differential equations in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    7. Yiheng Wei & Hamid Reza Karimi & Jinwen Pan & Qing Gao & Yong Wang, 2014. "Observation of a Class of Disturbance in Time Series Expansion for Fractional Order Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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