Theory of Translation Closedness for Time Scales

Chao Wang is a doctor in mathematics and teaches at the department of mathematics in Yunnan University in China. His research focuses on the fields of nonlinear dynamic systems, control theory, fuzzy dynamic equations,fractional differential equations, bifurcation theory,nonlinear analysis and numerical modeling. Ravi P. Agarwal is a Professor at the Texas A&M University in Kingsville, USA. He is also a Distinguished University Professor of Mathematics at the Florida Institute of Technology, Melbourne, FL, USA. He completed his PhD at the Indian Institute of Technology, India. Dr. Agarwal has authored, co-authored or co-edited over 60 books, including "An Introduction to Ordinary Differential Equations" (978-9-387-71275-8) and "Ordinary and Partial Differential Equations" (978-0-387-79145-6), both co-authored by Donal O`Regan and published by Springer. Donal O'Regan is a Professor at the School of Mathematics of the National University of Ireland. His research interests are in nonlinear functional analysis. His previous publications with Springer include "Constant-Sign Solutions of Systems of Integral Equations" (978-3-319-01254-4) and "Fixed Point Theory for Lipschitzian-type Mappings with Applications" (978-0-387-75817-6), both as a co-author. Rathinasamy Sakthivel is a Professor at the Department of Applied Mathematics, Bharathiar University, India. He completed his Ph.D. at Bharathiar University, India. His research focuses on the fields of systems and control theory, differential and integral equations, fractional differential equations and numerical methods for PDEs. He is an active editorial board member of several journals, including IEEE Access, Journal of the Franklin Institute, Neurocomputing, Journal of Electrical Engineering & Technology and Advances in Difference equations.

Preface.- Preliminaries and Basic Knowledge on Time Scales.- A Classification of Closedness of Time Scales under Translations.- Almost Periodic Functions and Generalizations on Complete-Closed Time Scales.- Piecewise Almost Periodic Functions and Generalizations on Translation Time Scales.- Almost Automorphic Functions and Generalizations on Translation Time Scales.- Nonlinear Dynamic Equations on Translation Time Scales.-  Impulsive Dynamic Equations on Translation Time Scales.- Almost Automorphic Dynamic Equations on Translation Time Scales.- Analysis of Dynamical System Models on Translation Time Scales.- Index.