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Stability in Nonlinear Neutral Caputo q -Fractional Difference Equations

Author

Listed:
  • Mouataz Billah Mesmouli

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia)

  • Abdelouaheb Ardjouni

    (Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras 41000, Algeria)

Abstract

In this article, we consider a nonlinear neutral q -fractional difference equation. So, we apply the fixed point theorem of Krasnoselskii to obtain the existence of solutions under sufficient conditions. After that, we use the fixed point theorem of Banach to show the uniqueness, as well as the stability of solutions. Our main results extend and generalize previous results mentioned in the conclusion.

Suggested Citation

  • Mouataz Billah Mesmouli & Abdelouaheb Ardjouni, 2022. "Stability in Nonlinear Neutral Caputo q -Fractional Difference Equations," Mathematics, MDPI, vol. 10(24), pages 1-9, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4763-:d:1004058
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    References listed on IDEAS

    as
    1. Thabet Abdeljawad & Betül Benli & Dumitru Baleanu, 2012. "A Generalized q -Mittag-Leffler Function by q -Captuo Fractional Linear Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, May.
    2. Fulai Chen & Zhigang Liu, 2012. "Asymptotic Stability Results for Nonlinear Fractional Difference Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, March.
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