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Existence and partial approximate controllability of nonlinear Riemann–Liouville fractional systems of higher order

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  • Haq, Abdul
  • Sukavanam, N.

Abstract

This article studies the existence and partial approximate controllability of higher order nonlocal semilinear fractional differential equations with Riemann–Liouville derivatives avoiding Lipschitz assumptions of nonlinear operator and nonlocal functions. To derive the existence result, we make approximate systems corresponding to the original system. For this, we construct the mild solutions in terms of fractional resolvent. Then, we prove the partial approximate controllability of the nonlinear system by using the obtained existence result. Finally, we give an example to illustrate the established theory.

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  • Haq, Abdul & Sukavanam, N., 2022. "Existence and partial approximate controllability of nonlinear Riemann–Liouville fractional systems of higher order," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p1:s0960077922009626
    DOI: 10.1016/j.chaos.2022.112783
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    References listed on IDEAS

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    1. Shouguo Zhu & Zhenbin Fan & Gang Li, 2017. "Optimal Controls for Riemann–Liouville Fractional Evolution Systems without Lipschitz Assumption," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 47-64, July.
    2. 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).
    3. Zhan-Dong Mei & Ji-Gen Peng & Yang Zhang, 2015. "An operator theoretical approach to Riemann-Liouville fractional Cauchy problem," Mathematische Nachrichten, Wiley Blackwell, vol. 288(7), pages 784-797, May.
    4. Haq, Abdul & Sukavanam, N., 2020. "Existence and approximate controllability of Riemann-Liouville fractional integrodifferential systems with damping," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. 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).
    6. Haq, Abdul, 2022. "Partial-approximate controllability of semi-linear systems involving two Riemann-Liouville fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    7. 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).
    8. Mahmudov, N.I., 2018. "Partial-approximate controllability of nonlocal fractional evolution equations via approximating method," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 227-238.
    9. Afreen, A. & Raheem, A. & Khatoon, A., 2022. "Controllability of a second-order non-autonomous stochastic semilinear system with several delays in control," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    10. Boudjerida, Assia & Seba, Djamila, 2021. "Approximate controllability of hybrid Hilfer fractional differential inclusions with non-instantaneous impulses," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    11. Yang, Min & Wang, Qiru, 2016. "Approximate controllability of Riemann–Liouville fractional differential inclusions," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 267-281.
    12. Li, Xuemei & Liu, Xinge & Tang, Meilan, 2021. "Approximate controllability of fractional evolution inclusions with damping," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
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    Cited by:

    1. Saha, Kiran Kumar & Sukavanam, N., 2023. "Existence and uniqueness of blow-up solution to a fully fractional thermostat model," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Malik, Muslim & Vijayakumar, V. & Shukla, Anurag, 2023. "Controllability of discrete-time semilinear Riemann–Liouville-like fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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