This book is devoted to a systematic and comprehensive study of existence, stability, boundary value problems, oscillatory behavior, and linear systems associated with generalized quantum impulsive differential equations. Generalized β-Impulsive Equations aims to provide both a rigorous theoretical foundation and practical analytical tools for researchers, graduate students, and specialists working in nonlinear analysis, dynamic equations, and applied mathematics.

In recent decades, the rapid development of quantum calculus—calculus without limits—together with the theory of impulsive differential equations has opened new and fertile directions for research. The synthesis of these two domains has led to the emergence of generalized quantum impulsive differential equations, a field that captures both discrete–continuous hybrid behavior and sudden state changes within a non-classical calculus setting.

This book aims to provide both a rigorous theoretical foundation and practical analytical tools for researchers, graduate students, and specialists working in nonlinear analysis, dynamic equations, and applied mathematics.