Existence and Hyers–Ulam Stability of Solutions for a Mixed Fractional-Order Nonlinear Delay Difference Equation with Parameters

Abstract

This paper focuses on a kind of mixed fractional-order nonlinear delay difference equations with parameters. Under some new criteria and by applying the Brouwer theorem and the contraction mapping principle, the new existence and uniqueness results of the solutions have been established. In addition, we deduce that the solution of the addressed equation is Hyers–Ulam stable. Some results in the literature can be generalized and improved. As an application, three typical examples are delineated to demonstrate the effectiveness of our theoretical results.

On Tempered (κ, ψ)-Hilfer Fractional Boundary Value Problems

“…This theme is pervasive in resources such as the book authored by Benchohra et al [4]. Research conducted by Luo et al [18] and Rus [25] has also delved into the stability of operatorial equations using the Ulam-Hyers methodology.…”

Existence, Uniqueness and Ulam-Hyers-Rassias Stability of Differential Coupled Systems with Riesz-Caputo Fractional Derivative

“…In 1978, Rassias [24] demonstrated the existence of unique linear mappings near approximate additive mappings, generalizing Hyers' findings. Several research articles in the literature address the Ulam stabilities of various types of differential and integral equations, see [19,21,31] and the references therein.…”

Existence and stability results for implicit impulsive convex combined Caputo fractional differential equations

“…One may see the papers [25,15,19,8], and the references therein. Several papers in the literature discuss the Ulam stabilities of various types of differential and integral equations, see [17,22,24,16,27,30,28,29] and the references therein.…”