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Controllability of semilinear noninstantaneous impulsive ABC neutral fractional differential equations

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  • Balasubramaniam, P.

Abstract

In this paper, the necessary and sufficient conditions are derived for the controllability of Atangana-Baleanu-Caputo (ABC) neutral fractional differential equations (FDEs) with noninstantaneous (NI) impulses. The main controllability result is obtained by using the concept of measure of noncompactness, semigroup, fractional calculus, and K-set contraction principle. An illustration is provided to validate the established theoretical result.

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  • Balasubramaniam, P., 2021. "Controllability of semilinear noninstantaneous impulsive ABC neutral fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921006305
    DOI: 10.1016/j.chaos.2021.111276
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    References listed on IDEAS

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    1. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
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    5. Ravichandran, C. & Logeswari, K. & Jarad, Fahd, 2019. "New results on existence in the framework of Atangana–Baleanu derivative for fractional integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 194-200.
    6. Bas, Erdal & Ozarslan, Ramazan, 2018. "Real world applications of fractional models by Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 121-125.
    7. Jean-Daniel Djida & Gisèle Mophou & Iván Area, 2019. "Optimal Control of Diffusion Equation with Fractional Time Derivative with Nonlocal and Nonsingular Mittag-Leffler Kernel," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 540-557, August.
    8. Kumar, Ashish & Pandey, Dwijendra N., 2020. "Existence of mild solution of Atangana–Baleanu fractional differential equations with non-instantaneous impulses and with non-local conditions," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    9. Aimene, D. & Baleanu, D. & Seba, D., 2019. "Controllability of semilinear impulsive Atangana-Baleanu fractional differential equations with delay," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 51-57.
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    Cited by:

    1. Balasubramaniam, P., 2022. "Solvability of Atangana-Baleanu-Riemann (ABR) fractional stochastic differential equations driven by Rosenblatt process via measure of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Ahmed, Hamdy M., 2022. "Construction controllability for conformable fractional stochastic evolution system with noninstantaneous impulse and nonlocal condition," Statistics & Probability Letters, Elsevier, vol. 190(C).
    3. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Nisar, Kottakkaran Sooppy & Shukla, Anurag, 2022. "A note concerning to approximate controllability of Atangana-Baleanu fractional neutral stochastic systems with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    4. 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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