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© 2020

Theory of Translation Closedness for Time Scales

With Applications in Translation Functions and Dynamic Equations

Book

Part of the Developments in Mathematics book series (volume 62)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Chao Wang, Ravi P. Agarwal, Donal O’Regan, Rathinasamy Sakthivel
    Pages 1-50
  3. Chao Wang, Ravi P. Agarwal, Donal O’Regan, Rathinasamy Sakthivel
    Pages 51-167
  4. Chao Wang, Ravi P. Agarwal, Donal O’Regan, Rathinasamy Sakthivel
    Pages 169-237
  5. Chao Wang, Ravi P. Agarwal, Donal O’Regan, Rathinasamy Sakthivel
    Pages 239-281
  6. Chao Wang, Ravi P. Agarwal, Donal O’Regan, Rathinasamy Sakthivel
    Pages 283-336
  7. Chao Wang, Ravi P. Agarwal, Donal O’Regan, Rathinasamy Sakthivel
    Pages 337-387
  8. Chao Wang, Ravi P. Agarwal, Donal O’Regan, Rathinasamy Sakthivel
    Pages 389-476
  9. Chao Wang, Ravi P. Agarwal, Donal O’Regan, Rathinasamy Sakthivel
    Pages 477-504
  10. Chao Wang, Ravi P. Agarwal, Donal O’Regan, Rathinasamy Sakthivel
    Pages 505-561
  11. Back Matter
    Pages 563-577

About this book

Introduction

This monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S. Hilger in 1988 to unify continuous and discrete analysis. The authors develop a theory of translation function on time scales that contains (piecewise) almost periodic functions, (piecewise) almost automorphic functions and their related generalization functions (e.g., pseudo almost periodic functions, weighted pseudo almost automorphic functions, and more). Against the background of dynamic equations, these function theories on time scales are applied to study the dynamical behavior of solutions for various types of dynamic equations on hybrid domains, including evolution equations, discontinuous equations and impulsive integro-differential equations.

The theory presented allows many useful applications, such as in the Nicholson`s blowfiles model; the Lasota-Wazewska model; the Keynesian-Cross model; in those realistic dynamical models with a more complex hibrid domain, considered under different types of translation closedness of time scales; and in dynamic equations on mathematical models which cover neural networks. This book provides readers with the theoretical background necessary for accurate mathematical modeling in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, and social sciences.

Keywords

time scales almost periodic functions automorphic functions translation functions translation time scales impulsive dynamic equations automorphic dynamic equations system models Hilger Bohr transform Cauchy matrix Liouville's formula Lasota-Wazewska model 34N05 43A60 42A75 93A30

Authors and affiliations

  1. 1.Department of MathematicsYunnan UniversityKunmingChina
  2. 2.Department of MathematicsTexas A&M University—KingsvilleKingsvilleUSA
  3. 3.School of Mathematics, Statistics and Applied MathematicsNational University of IrelandGalwayIreland
  4. 4.Department of Applied MathematicsBharathiar UniversityCoimbatoreIndia

About the authors

Chao Wang is an associate professor and 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 Engineer.

Bibliographic information