A New Wendroff-Type Weakly Singular Integral Inequality and Applications to Partial Fractional Differential Equations

Abstract

In this paper, we establish a novel weakly singular integral inequality of Wendroff type. Using a combination of analytical and fractional calculus techniques, we derive sufficient conditions for the validity of this inequality. As a key application, we investigate the existence, uniqueness, and Ulam-Hyers stability of solutions to a class of nonlinear partial fractional differential equations. Our approach not only generalizes previous results but also provides a unified framework for analyzing fractional-order systems with singular kernels. An illustrative example is presented to demonstrate the applicability and effectiveness of the proposed method.