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Approximate controllability of hybrid Hilfer fractional differential inclusions with non-instantaneous impulses

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  • Boudjerida, Assia
  • Seba, Djamila

Abstract

This paper deals with the approximate controllability of a class of non-instantaneous impulsive hybrid systems for fractional differential inclusions under Hilfer derivative of order 1<σ<2 and type 0≤ζ≤1, on weighted spaces. As an alternative to the Wright function which is defined only when 0<σ<1, we make use of a family of general fractional resolvent operators to give a proper form of the mild solution. This latter is consequently formulated by Laplace transform, improving and extending important results on this topic. Based on known facts about fractional calculus and set-valued maps, properties of the resolvent operator, and a hybrid fixed point theorem for three operators of Schaefer type, the existence result and the approximate controllability of our system is achieved. An example is given to demonstrate the effectiveness of our result.

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  • Boudjerida, Assia & Seba, Djamila, 2021. "Approximate controllability of hybrid Hilfer fractional differential inclusions with non-instantaneous impulses," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004793
    DOI: 10.1016/j.chaos.2021.111125
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    References listed on IDEAS

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    1. Gu, Haibo & Trujillo, Juan J., 2015. "Existence of mild solution for evolution equation with Hilfer fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 344-354.
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    4. Raja, M. Mohan & Vijayakumar, V. & Udhayakumar, R. & Zhou, Yong, 2020. "A new approach on the approximate controllability of fractional differential evolution equations of order 1 < r < 2 in Hilbert spaces," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    5. Sutar, Sagar T. & Kucche, Kishor D., 2021. "On Nonlinear Hybrid Fractional Differential Equations with Atangana-Baleanu-Caputo Derivative," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. Mohammed M. Matar, 2019. "Approximate Controllability of Fractional Nonlinear Hybrid Differential Systems via Resolvent Operators," Journal of Mathematics, Hindawi, vol. 2019, pages 1-7, March.
    7. 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:

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    2. Haq, Abdul, 2022. "Partial-approximate controllability of semi-linear systems involving two Riemann-Liouville fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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