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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 pth 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, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:769257
    DOI: 10.1155/2013/769257
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    References listed on IDEAS

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    1. Sakthivel, R. & Luo, J., 2009. "Asymptotic stability of nonlinear impulsive stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1219-1223, May.
    2. Chen, Huabin, 2010. "Impulsive-integral inequality and exponential stability for stochastic partial differential equations with delays," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 50-56, January.
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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. 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).
    3. 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).
    4. 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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