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Existence and data dependence theorems for solutions of an ABC-fractional order impulsive system

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  • Khan, Hasib
  • Khan, Aziz
  • Jarad, Fahd
  • Shah, Anwar

Abstract

The study of existence of solution ensures the essential conditions required for a solution. Keeping the importance of the study, we initiate the existence, uniqueness and data dependence of solutions an Atangana-Baleanu-Caputo (ABC)-fractional order differential impulsive system. For this purpose, the suggested ABC-fractional order differential impulsive system is transferred into equivalent fixed point problem via integral operator. The operator is then analyzed for boundedness, continuity and equicontinuity. Then Arzela-Ascolli theorem ensures the relatively compactness of the operator and the Schauder’s fixed point theorem and Banach’s fixed point theorem are utilized for the existence and uniqueness of solution. Data dependence and expressive application are also provided.

Suggested Citation

  • Khan, Hasib & Khan, Aziz & Jarad, Fahd & Shah, Anwar, 2020. "Existence and data dependence theorems for solutions of an ABC-fractional order impulsive system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304230
    DOI: 10.1016/j.chaos.2019.109477
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    References listed on IDEAS

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    1. Abdeljawad, Thabet & Al-Mdallal, Qasem M. & Jarad, Fahd, 2019. "Fractional logistic models in the frame of fractional operators generated by conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 94-101.
    2. Jarad, Fahd & Abdeljawad, Thabet & Hammouch, Zakia, 2018. "On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 16-20.
    3. 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.
    4. Alqahtani, Badr & Fulga, Andreea & Jarad, Fahd & Karapınar, Erdal, 2019. "Nonlinear F-contractions on b-metric spaces and differential equations in the frame of fractional derivatives with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 349-354.
    5. 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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    3. 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).

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