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Moment stability via resolvent operators of fractional stochastic differential inclusions driven by fractional Brownian motion

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  • Tamilalagan, P.
  • Balasubramaniam, P.

Abstract

In this manuscript, we consider a class of fractional stochastic differential inclusions driven by fractional Brownian motion in Hilbert space with Hurst parameter H^∈(12,1). Sufficient conditions for the existence and asymptotic stability of mild solutions are derived in mean square moment by employing fractional calculus, analytic resolvent operators and Bohnenblust–Karlin’s fixed point theorem. The effectiveness of the obtained theoretical results is illustrated by an example.

Suggested Citation

  • Tamilalagan, P. & Balasubramaniam, P., 2017. "Moment stability via resolvent operators of fractional stochastic differential inclusions driven by fractional Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 299-307.
    • Handle: RePEc:eee:apmaco:v:305:y:2017:i:c:p:299-307
    DOI: 10.1016/j.amc.2017.02.013
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    References listed on IDEAS

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    1. Boufoussi, Brahim & Hajji, Salah, 2012. "Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1549-1558.
    2. Balasubramaniam, P. & Tamilalagan, P., 2015. "Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi’s function," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 232-246.
    3. Lei Zhang & Yongsheng Ding & Kuangrong Hao & Liangjian Hu & Tong Wang, 2014. "Moment stability of fractional stochastic evolution equations with Poisson jumps," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(7), pages 1539-1547, July.
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    5. Ge, Fudong & Kou, Chunhai, 2015. "Stability analysis by Krasnoselskii’s fixed point theorem for nonlinear fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 308-316.
    6. Couillard, Michel & Davison, Matt, 2005. "A comment on measuring the Hurst exponent of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 404-418.
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    Cited by:

    1. Dhayal, Rajesh & Malik, Muslim, 2021. "Approximate controllability of fractional stochastic differential equations driven by Rosenblatt process with non-instantaneous impulses," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Irshad Ahmad & Saeed Ahmad & Ghaus ur Rahman & Shabir Ahmad & Manuel De la Sen, 2022. "Controllability and Observability Results of an Implicit Type Fractional Order Delay Dynamical System," Mathematics, MDPI, vol. 10(23), pages 1-24, November.
    3. Hamdy M. Ahmed & Mahmoud M. El-Borai & Hassan M. El-Owaidy & Ahmed S. Ghanem, 2019. "Existence Solution and Controllability of Sobolev Type Delay Nonlinear Fractional Integro-Differential System," Mathematics, MDPI, vol. 7(1), pages 1-14, January.
    4. Vijayakumar, V. & Udhayakumar, R., 2020. "Results on approximate controllability for non-densely defined Hilfer fractional differential system with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Ahmed, Hamdy M. & Zhu, Quanxin, 2023. "Exploration nonlocal controllability for Hilfer fractional differential inclusions with Clarke subdifferential and nonlinear noise," Statistics & Probability Letters, Elsevier, vol. 195(C).

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