Theory of Translation Closedness for Time Scales With Applications in Translation Functions and Dynamic Equations

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Synopsis

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.

Book details

Edition:
1st ed. 2020
Series:
Developments in Mathematics (Book 62)
Author:
Chao Wang, Ravi P. Agarwal, Rathinasamy Sakthivel, Donal O' Regan
ISBN:
9783030386443
Related ISBNs:
9783030386436
Publisher:
Springer International Publishing
Pages:
N/A
Reading age:
Not specified
Includes images:
Yes
Date of addition:
2020-05-30
Usage restrictions:
Copyright
Copyright date:
2020
Copyright by:
Springer Nature Switzerland AG 
Adult content:
No
Language:
English
Categories:
Mathematics and Statistics, Nonfiction