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Asymptotic stability of fractional order (1,2] stochastic delay differential equations in Banach spaces

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  • Singh, Ajeet
  • Shukla, Anurag
  • Vijayakumar, V.
  • Udhayakumar, R.

Abstract

In this article, we discuss the asymptotic stability and mean square stability of stochastic differential equations of fractional-order 1<α≤2. We have considered the family of stochastic differential equations with variable delay in the state. For proving our main results, we apply the Banach fixed point theorem and imposed the Lipschitz condition on nonlinearity. Finally, we present an example to illustrate the obtained theory.

Suggested Citation

  • 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).
  • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004495
    DOI: 10.1016/j.chaos.2021.111095
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    References listed on IDEAS

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    7. Raja, M. Mohan & Vijayakumar, V. & Udhayakumar, R. & Zhou, Yong, 2020. "A new approach on the approximate controllability of fractional differential evolution equations of order 1 < r < 2 in Hilbert spaces," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    Cited by:

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    2. Kavitha, K. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy & Udhayakumar, R., 2021. "Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Shukla, Anurag & Vijayakumar, V. & Nisar, Kottakkaran Sooppy, 2022. "A new exploration on the existence and approximate controllability for fractional semilinear impulsive control systems of order r∈(1,2)," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
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    5. Chendur Kumaran, R. & Venkatesh, T.G. & Swarup, K.S., 2022. "Stochastic delay differential equations: Analysis and simulation studies," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
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    7. Gautam, Pooja & Shukla, Anurag, 2023. "Stochastic controllability of semilinear fractional control differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    8. Lu Zhang & Caishi Wang & Jinshu Chen, 2023. "Interacting Stochastic Schrödinger Equation," Mathematics, MDPI, vol. 11(6), pages 1-16, March.
    9. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy, 2021. "A note on approximate controllability for nonlocal fractional evolution stochastic integrodifferential inclusions of order r∈(1,2) with delay," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
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