Stability Analysis of a Fractional Order Discrete Anti-Periodic Boundary Value Problem

Abstract

This article aims at investigating stability properties for a class of discrete fractional equations with anti-periodic boundary conditions of fractional order δ ∈ (3, 4]. Utilizing contraction mapping principle and fixed point theorem due to Brouwer [2], new criteria for the uniqueness and existence of the solutions are developed and two types of Ulam stability are analyzed. The theoretical outcomes are corroborated with examples.

Novel Results for the Stability of h-Discrete Fractional Neural Networks with Nonsingular and Nonlocal Kernels

“…In discrete-time equations and systems, the Ulam-Hyers stability has also been steadily evolved. The Ulam-Hyers stability of a family of discrete fractional equations with antiperiodic boundary conditions was discussed in [31]. In [32] the stability of nonlinear discrete fractional initial value problems with application to vibrating eardrum in the sens of Ulam-Hyers stability was investigated, [33] provides Ulam-Hyers stability results for Caputo nabla fractional difference equations in both linear and nonlinear cases, while [34] demonstrated the existence and Ulam-Hyers stability of solutions for an initial value discrete fractional Duffing equation with a forcing term.…”

Analysis of Fractional Order Differential Equation Using Laplace Transform

“…Also, Sabatier et al [14] established the stability conditions for fractional order system by utilizing Laplace transform. The existence and stability of fractional order difference equations with certain boundary conditions is discussed by Selvam et al [17]. Also, Liang et al [12], Ye et al [20], and Deng et al [6] have used the Laplace transform method to analyze certain qualitative properties of FODE.…”