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Nonlinear F-contractions on b-metric spaces and differential equations in the frame of fractional derivatives with Mittag–Leffler kernel

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  • Alqahtani, Badr
  • Fulga, Andreea
  • Jarad, Fahd
  • Karapınar, Erdal

Abstract

In this manuscript, we aim to refine and characterize nonlinear F-contractions in a more general framework of b-metric spaces. We investigate the existence and uniqueness of such contractions in this setting. We discuss the solutions to differential equations in the setting of fractional derivatives involving Mittag–Leffler kernels (Atangana–Baleanu fractional derivative) by using nonlinear F-contractions that indicate the genuineness of the presented result.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:128:y:2019:i:c:p:349-354
    DOI: 10.1016/j.chaos.2019.08.002
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. 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).
    2. Logeswari, K. & Ravichandran, C., 2020. "A new exploration on existence of fractional neutral integro- differential equations in the concept of Atangana–Baleanu derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).

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