Stability in Nonlinear Neutral Caputo q -Fractional Difference Equations

Mouataz Billah Mesmouli () and Abdelouaheb Ardjouni
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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

Mathematics, 2022, vol. 10, issue 24, 1-9

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.

Keywords: stability; q -fractional difference equations; Krasnoselskii fixed point theorem; contraction; Arzela–Ascoli’s theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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