Schauder’s fixed point theorem approach for stability analysis of nonlinear fractional difference equations

Anshul Sharma, S.N. Mishra and Anurag Shukla

Chaos, Solitons & Fractals, 2024, vol. 188, issue C

Abstract: Analyzing the stability of solutions is a key qualitative aspect of discrete fractional calculus, with many applications. This paper explores a type of discrete equation that incorporates a Hilfer-like fractional difference. We use Picard’s iteration method and Schauder’s fixed point theorem to establish results concerning the existence and uniqueness of solutions. Additionally, we examine both attractive stability and Ulam–Hyers stability for the proposed system. To illustrate our findings, we provide three examples that demonstrate how the main results are verified.

Keywords: Hilfer-like discrete operator; Attractive stability; Ulam–Hyers stability; Fixed point theorems; Newton iteration method (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:188:y:2024:i:c:s096007792401138x

DOI: 10.1016/j.chaos.2024.115586

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