On the Stability of Partial Integral Equations Governed by Hadamard Fractional Integrals of Piecewise Constant Order

Abstract

This article investigates the existence and global stability of a class of partial integral equations involving the Hadamard fractional integral of variable order. By employing Schauder's fixed point theorem within appropriately constructed function spaces, we establish sufficient conditions ensuring the existence of solutions. We also analyze the asymptotic behavior of these solutions and derive criteria that guarantee their global asymptotic stability. The practical relevance of the theoretical results is demonstrated through a detailed example that highlights the applicability and effectiveness of the proposed approach. Overall, this study provides foundational insights into the existence and stability properties of a recently introduced class of fractional integral equations, representing one of the first investigations conducted within this mathematical framework.