This book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations.

Chapter 1- Calculus on Time Scales.- Chapter 2- Dynamic Systems.- Chapter 3- Functional Dynamic Equations. Basic Concepts, Existence and Uniqueness Theorems.- Chapter 4- Linear Functional Dynamic Equations.- Chapter 5- Stability for First Order Functional Dynamic Equations.- Chapter 6- Oscillations of First Order Functional Dynamic Equations.- Chapter 7- Oscillations of Second Order Linear Functional Dynamic Equations  with a Single Delay.- Chapter 8- Nonoscillations of Second Order Functional Dynamic Equations with  Several Delays.- Chapter 9- Oscillations of Second Order Nonlinear Functional Dynamic Equations.- Chapter 10- Oscillations of Third Order Functional Dynamic Equations.- Chapter 11- Oscillations of Fourth Order Functional Dynamic Equations.- Chapter 12- Oscillations of Higher Order Functional Dynamic Equations.- Chapter 13- Shift Operators.- Chapter 14- Impulsive Functional Dynamic Equations.- Chapter 15- Linear Impulsive Dynamic Systems.- Appendix: Fréchet Derivatives and Gâteaux.- Appendix: Pötzsche’s Chain Rule.- Appendix: The Knaster-Tarski Fixed Point Theorem.- Appendix: Some Elementary Inequalities.- Knesser’s Theorem.- References.- Index

This book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations. It discusses functional dynamic equations in relation to mathematical physics applications and problems, providing useful tools for investigation for oscillations and nonoscillations of the solutions of functional dynamic equations on time scales. Practice problems are presented throughout the book for use as a graduate-level textbook and as a reference book for specialists of several disciplines, such as mathematics, physics, engineering, and biology.

“This is a complete and interesting book concerning functional dynamic equations on time scales. This book has 15 chapters and 5 appendixes, there are almost 900 pages with a precious content of the theory of time scales ... . This book will be very useful for all mathematicians that work with theory of time scales ... . Also, it can be used as a reference in courses of graduate level.” (Jaqueline Godoy Mesquita, zbMATH 1510.34001, 2023)

This books offers the reader an overview of recent developments of functional dynamic equations on time scales, taking readers beyond the traditional calculus texts. The book introduces functional dynamic equations in relation to mathematical physics applications and problems. Useful tools are provided for investigation for oscillations and nonoscillations of the solutions of functional dynamic equations on time scales. This book is suitable for graduate courses and researchers looking for an introduction to functional dynamic equations on time scales.

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