Husam E. Dargail

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.

This study looks at the stability and stabilization issues concerning the nonlinear time-delay systems specified by conformable derivatives. These requirements can be used for many useful applications. Through the construction of appropriate Lyapunov–Krasovskii functionals, we develop novel linear matrix inequality (LMI) conditions for the exponential stability of autonomous systems and practical exponential stability for systems subject to bounded perturbations. Furthermore, we propose state-feedback stabilization strategies that transform the controller design problem into a convex optimization framework solvable via efficient LMI techniques. The theoretical developments are comprehensively validated through numerical examples that demonstrate the effectiveness of the proposed stability and stabilization criteria. The results establish a rigorous framework for analyzing and controlling conformable fractional-order systems with time delays, bridging theoretical advances with practical implementation considerations.

This paper investigates the stability analysis and stabilization problems for a class of nonlinear time-delay systems described by conformable derivatives. We consider systems with one-sided Lipschitz nonlinearities and quadratic inner-boundedness conditions, which encompass a broad range of practical applications. Through the construction of appropriate Lyapunov-Krasovskii functionals, we develop novel linear matrix inequality (LMI) conditions for exponential stability of autonomous systems and practical exponential stability for systems subject to bounded perturbations. Furthermore, we propose state-feedback stabilization strategies that transform the controller design problem into a convex optimization framework solvable via efficient LMI techniques. The theoretical developments are comprehensively validated through numerical examples that demonstrate the effectiveness of the proposed stability and stabilization criteria. The results establish a rigorous framework for analyzing and controlling conformable fractional-order systems with time delays, bridging theoretical advances with practical implementation considerations.