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Stochastic controllability of semilinear fractional control differential equations

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  • Gautam, Pooja
  • Shukla, Anurag

Abstract

The purpose of our research is to identify some sufficient conditions for the stochastic controllability of fractional-order semilinear stochastic systems. The required outcomes are achieved by dividing the system under consideration into two systems: a linear stochastic system and a semilinear deterministic system. The key outcomes are achieved by employing the Schauder fixed point technique, nonlinear monotonicity, and keeping just fractional-order α∈(1/2,1). One example is presented for demonstrating the outcomes.

Suggested Citation

  • Gautam, Pooja & Shukla, Anurag, 2023. "Stochastic controllability of semilinear fractional control differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007592
    DOI: 10.1016/j.chaos.2023.113858
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    References listed on IDEAS

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    1. P. Balasubramaniam & J. P. Dauer, 2001. "Controllability of semilinear stochastic evolution equations in Hilbert space," International Journal of Stochastic Analysis, Hindawi, vol. 14, pages 1-11, January.
    2. 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).
    3. Sivashankar, M. & Sabarinathan, S. & Nisar, Kottakkaran Sooppy & Ravichandran, C. & Kumar, B.V. Senthil, 2023. "Some properties and stability of Helmholtz model involved with nonlinear fractional difference equations and its relevance with quadcopter," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    4. Raja, M. Mohan & Vijayakumar, V. & Udhayakumar, R., 2020. "A new approach on approximate controllability of fractional evolution inclusions of order 1 < r < 2 with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    5. 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).
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    Cited by:

    1. Dineshkumar, Chendrayan & Jeong, Jae Hoon & Joo, Young Hoon, 2024. "Stochastic exponential stabilization and optimal control results for a class of fractional order equations," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).

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