ABSTRACT
This introduction presents an overview of the key concepts covered in the subsequent chapters of this book. The book considers impulsive systems of Caputo-type fractional functional differential equations with fixed moments of impulse effect. It presents the main classes of Lyapunov functions that will be used in the qualitative investigation of fractional-order systems. The book also considers fractional scalar and vector comparison results in terms of Lyapunov-like functions. It aims to contribute to the development of the Lyapunov theory, presenting Razumikhin-type stability theorems. The book offers Lyapunov stability, Mittag–Leffler stability and boundedness definitions, as well as definitions for almost periodic sequences and almost periodic functions. It utilizes the Mittag–Leffler function which plays an important role in the theory of non-integer order differential equations. It is well-known that the delay differential equations of integer order are of great theoretical interest and form an important class as regards to their applications.
