Fixed-Point Approaches to Stability and Existence in Nonlinear $\psi$-Caputo Fractional Systems

Abstract

The primary objective of this study is to derive existence results and stability criteria for a class of
fractional-order differential equations by employing fixed point theorems. The existence results are established
using Schauder's fixed point theorem and the Banach contraction principle, which provide a solid theoretical
foundation for analyzing such equations. Special emphasis is placed on the application of Krasnoselskii's
fixed point theorem to determine stability criteria for a specific class of fractional-order differential equations,
offering a novel approach to addressing stability concerns in this context. To illustrate the practical
relevance of the theoretical findings, an example is provided, demonstrating the effectiveness and applicability
of the derived stability result in real-world scenarios.