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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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    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. Long, Shaohua & Zhang, Yu & Zhong, Shouming, 2024. "New results on the stability and stabilization for singular neutral systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    3. 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).
    4. Hammad, Hasanen A. & Alshehri, Maryam G., 2024. "Application of the Mittag-Leffler kernel in stochastic differential systems for approximating the controllability of nonlocal fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    5. 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).
    6. 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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