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Nonlocal impulsive fractional differential inclusions with fractional sectorial operators on Banach spaces

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  • Wang, JinRong
  • Ibrahim, Ahmed Gamal
  • Fečkan, Michal

Abstract

This paper investigates existence of PC-mild solutions of impulsive fractional differential inclusions with nonlocal conditions when the linear part is a fractional sectorial operators like in Bajlekova (2001) [1] on Banach spaces. We derive two existence results of PC-mild solutions when the values of the semilinear term F is convex as well as another existence result when its values are nonconvex. Further, the compactness of the set of solutions is characterized.

Suggested Citation

  • Wang, JinRong & Ibrahim, Ahmed Gamal & Fečkan, Michal, 2015. "Nonlocal impulsive fractional differential inclusions with fractional sectorial operators on Banach spaces," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 103-118.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:103-118
    DOI: 10.1016/j.amc.2014.04.093
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    References listed on IDEAS

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    1. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
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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. Selvaraj Suganya & Mani Mallika Arjunan, 2017. "Existence of Mild Solutions for Impulsive Fractional Integro-Differential Inclusions with State-Dependent Delay," Mathematics, MDPI, vol. 5(1), pages 1-16, January.
    3. Chen, Qian & Debbouche, Amar & Luo, Zijian & Wang, JinRong, 2017. "Impulsive fractional differential equations with Riemann–Liouville derivative and iterative learning control," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 111-118.
    4. Balasubramaniam, P., 2021. "Controllability of semilinear noninstantaneous impulsive ABC neutral fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Mohamed Hannabou & Hilal Khalid, 2019. "Investigation of a Mild Solution to Coupled Systems of Impulsive Hybrid Fractional Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2019, pages 1-9, December.
    6. Suganya, S. & Mallika Arjunan, M. & Trujillo, J.J., 2015. "Existence results for an impulsive fractional integro-differential equation with state-dependent delay," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 54-69.
    7. Debbouche, Amar & Antonov, Valery, 2017. "Approximate controllability of semilinear Hilfer fractional differential inclusions with impulsive control inclusion conditions in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 140-148.
    8. 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).
    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.
    10. Arjunan, Mani Mallika & Abdeljawad, Thabet & Anbalagan, Pratap, 2022. "Impulsive effects on fractional order time delayed gene regulatory networks: Asymptotic stability analysis," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    11. Wang, JinRong & Fĕckan, Michal & Zhou, Yong, 2017. "Center stable manifold for planar fractional damped equations," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 257-269.
    12. Lin, Zeng & Wang, JinRong & Wei, Wei, 2015. "Fractional differential equation models with pulses and criterion for pest management," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 398-408.
    13. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.

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