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Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type

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  • Kavitha, K.
  • Vijayakumar, V.
  • Shukla, Anurag
  • Nisar, Kottakkaran Sooppy
  • Udhayakumar, R.

Abstract

The basic motivation of this research paper is the approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type which generalized the Riemann-Liouville fractional derivative. Combining with the techniques of fractional calculus, fixed point theorem for multi-value dmaps and Sobolev-type and Clarke subdifferential to the approximate controllability system we obtain new existence result of mild solutions. Next, we demonstrate linear and semilinear systems for approximate controllability. Finally, to verify our theoretical results, an illustration is also included.

Suggested Citation

  • Kavitha, K. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy & Udhayakumar, R., 2021. "Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921006184
    DOI: 10.1016/j.chaos.2021.111264
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    References listed on IDEAS

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    1. 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).
    2. Lu, Liang & Liu, Zhenhai & Bin, Maojun, 2016. "Approximate controllability for stochastic evolution inclusions of Clarke’s subdifferential type," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 201-212.
    3. 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).
    4. Ravichandran, C. & Logeswari, K. & Panda, Sumati Kumari & Nisar, Kottakkaran Sooppy, 2020. "On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Michal Fec̆kan & JinRong Wang & Yong Zhou, 2013. "Controllability of Fractional Functional Evolution Equations of Sobolev Type via Characteristic Solution Operators," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 79-95, January.
    6. Kavitha, K. & Vijayakumar, V. & Udhayakumar, R., 2020. "Results on controllability of Hilfer fractional neutral differential equations with infinite delay via measures of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
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    Cited by:

    1. Mohan Raja, M. & Vijayakumar, V., 2022. "Existence results for Caputo fractional mixed Volterra-Fredholm-type integrodifferential inclusions of order r ∈ (1,2) with sectorial operators," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    2. 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).
    3. Asmae Tajani & Fatima-Zahrae El Alaoui, 2023. "Boundary Controllability of Riemann–Liouville Fractional Semilinear Evolution Systems," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 767-780, August.
    4. Kalimuthu, K. & Mohan, M. & Chokkalingam, R. & Nisar, Kottakkaran Sooppy, 2022. "Results on neutral differential equation of sobolev type with nonlocal conditions," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    5. 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).
    6. Zhang, Chuanlin & Ye, Guoju & Liu, Wei & Liu, Xuelong, 2024. "On controllability for Sobolev-type fuzzy Hilfer fractional integro-differential inclusions with Clarke subdifferential," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    7. Haq, Abdul, 2022. "Partial-approximate controllability of semi-linear systems involving two Riemann-Liouville fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    8. Mei-Qi, Wang & Wen-Li, Ma & En-Li, Chen & Yu-Jian, Chang & Cui-Yan, Wang, 2022. "Principal resonance analysis of piecewise nonlinear oscillator with fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

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