Nonlinear Integral Equations On Time Scales

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Integral Equations On Time Scales

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Author : Svetlin G. Georgiev
language : en
Publisher: Springer
Release Date : 2016-10-30

Integral Equations On Time Scales written by Svetlin G. Georgiev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-30 with Mathematics categories.

This book offers the reader an overview of recent developments of integral equations on time scales. It also contains elegant analytical and numerical methods. This book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. The students in mathematical and physical sciences will find many sections of direct relevance. The book contains nine chapters and each chapter is pedagogically organized. This book is specially designed for those who wish to understand integral equations on time scales without having extensive mathematical background.

Nonlinear Integral Equations On Time Scales

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Author : Svetlin G. Georgiev
language : en
Publisher:
Release Date : 2019-03-26

Nonlinear Integral Equations On Time Scales written by Svetlin G. Georgiev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-26 with categories.

This book presents an introduction to the theory of nonlinear integral equations on time scales. Many population discrete models such as the logistic model, the Ricker model, the Beverton-Holt model, Leslie-Gower competition model and others can be investigated using nonlinear integral equations on the set of the natural numbers. This book contains different analytical and numerical methods for investigation of nonlinear integral equations on time scales. It is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. Students in mathematical and physical sciences willfind many sections of direct relevance. This book contains nine chapters, and each chapter consists of numerous examples and exercises.

Integral Inequalities On Time Scales

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Author : Svetlin G. Georgiev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-08-24

Integral Inequalities On Time Scales written by Svetlin G. Georgiev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-24 with Mathematics categories.

This book is devoted to recent developments of linear and nonlinear integral inequalities on time scales. The book is intended for the use in the field of dynamic calculus on time scales, dynamic equation and integral equations on time scales. It is also suitable for graduate courses in the above fields. The book is designed for those who have mathematical background on time scales calculus.

Dynamic Equations On Time Scales

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Author : Martin Bohner
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-15

Dynamic Equations On Time Scales written by Martin Bohner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-15 with Language Arts & Disciplines categories.

The study of dynamic equations on a measure chain (time scale) goes back to its founder S. Hilger (1988), and is a new area of still fairly theoretical exploration in mathematics. Motivating the subject is the notion that dynamic equations on measure chains can build bridges between continuous and discrete mathematics. Further, the study of measure chain theory has led to several important applications, e.g., in the study of insect population models, neural networks, heat transfer, and epidemic models. Key features of the book: * Introduction to measure chain theory; discussion of its usefulness in allowing for the simultaneous development of differential equations and difference equations without having to repeat analogous proofs * Many classical formulas or procedures for differential and difference equations cast in a new light * New analogues of many of the "special functions" studied * Examination of the properties of the "exponential function" on time scales, which can be defined and investigated using a particularly simple linear equation * Additional topics covered: self-adjoint equations, linear systems, higher order equations, dynamic inequalities, and symplectic dynamic systems * Clear, motivated exposition, beginning with preliminaries and progressing to more sophisticated text * Ample examples and exercises throughout the book * Solutions to selected problems Requiring only a first semester of calculus and linear algebra, Dynamic Equations on Time Scales may be considered as an interesting approach to differential equations via exposure to continuous and discrete analysis. This approach provides an early encounter with many applications in such areas as biology, physics, and engineering. Parts of the book may be used in a special topics seminar at the senior undergraduate or beginning graduate levels. Finally, the work may

Dynamic Inequalities On Time Scales

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Author : Ravi Agarwal
language : en
Publisher: Springer
Release Date : 2014-10-30

Dynamic Inequalities On Time Scales written by Ravi Agarwal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-30 with Mathematics categories.

This is a monograph devoted to recent research and results on dynamic inequalities on time scales. The study of dynamic inequalities on time scales has been covered extensively in the literature in recent years and has now become a major sub-field in pure and applied mathematics. In particular, this book will cover recent results on integral inequalities, including Young's inequality, Jensen's inequality, Holder's inequality, Minkowski's inequality, Steffensen's inequality, Hermite-Hadamard inequality and Čebyšv's inequality. Opial type inequalities on time scales and their extensions with weighted functions, Lyapunov type inequalities, Halanay type inequalities for dynamic equations on time scales, and Wirtinger type inequalities on time scales and their extensions will also be discussed here in detail.

Integral Inequalities On Time Scales

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Author : Svetlin G. Georgiev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-08-24

Integral Inequalities On Time Scales written by Svetlin G. Georgiev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-24 with Mathematics categories.

This book is devoted to recent developments of linear and nonlinear integral inequalities on time scales. The book is intended for the use in the field of dynamic calculus on time scales, dynamic equation and integral equations on time scales. It is also suitable for graduate courses in the above fields. The book is designed for those who have mathematical background on time scales calculus.

Dynamic Calculus And Equations On Time Scales

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Author : Svetlin G. Georgiev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-09-18

Dynamic Calculus And Equations On Time Scales written by Svetlin G. Georgiev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-18 with Mathematics categories.

The latest advancements in time scale calculus are the focus of this book. New types of time-scale integral transforms are discussed in the book, along with how they can be used to solve dynamic equations. Novel numerical techniques for partial dynamic equations on time scales are described. New time scale inequalities for exponentially convex functions are introduced as well.

Boundary Value Problems On Time Scales Volume I

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Author : Svetlin Georgiev
language : en
Publisher: CRC Press
Release Date : 2021-10-14

Boundary Value Problems On Time Scales Volume I written by Svetlin Georgiev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-14 with Mathematics categories.

Boundary Value Problems on Time Scales, Volume I is devoted to the qualitative theory of boundary value problems on time scales. Summarizing the most recent contributions in this area, it addresses a wide audience of specialists such as mathematicians, physicists, engineers and biologists. It can be used as a textbook at the graduate level and as a reference book for several disciplines. The text contains two volumes, both published by Chapman & Hall/CRC Press. Volume I presents boundary value problems for first- and second-order dynamic equations on time scales. Volume II investigates boundary value problems for three, four, and higher-order dynamic equations on time scales. Many results to differential equations carry over easily to corresponding results for difference equations, while other results seem to be totally different in nature. Because of these reasons, the theory of dynamic equations is an active area of research. The time-scale calculus can be applied to any field in which dynamic processes are described by discrete or continuous time models. The calculus of time scales has various applications involving noncontinuous domains such as certain bug populations, phytoremediation of metals, wound healing, maximization problems in economics, and traffic problems. Boundary value problems on time scales have been extensively investigated in simulating processes and the phenomena subject to short-time perturbations during their evolution. The material in this book is presented in highly readable, mathematically solid format. Many practical problems are illustrated displaying a wide variety of solution techniques. AUTHORS Svetlin G. Georgiev is a mathematician who has worked in various areas of the study. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales. Khaled Zennir earned his PhD in mathematics in 2013 from Sidi Bel Abbès University, Algeria. In 2015, he received his highest diploma in Habilitation in mathematics from Constantine University, Algeria. He is currently assistant professor at Qassim University in the Kingdom of Saudi Arabia. His research interests lie in the subjects of nonlinear hyperbolic partial differential equations: global existence, blowup, and long-time behavior.

Stability Periodicity And Boundedness In Functional Dynamical Systems On Time Scales

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Author : Murat Adıvar
language : en
Publisher: Springer Nature
Release Date : 2020-04-23

Stability Periodicity And Boundedness In Functional Dynamical Systems On Time Scales written by Murat Adıvar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-23 with Mathematics categories.

Motivated by recent increased activity of research on time scales, the book provides a systematic approach to the study of the qualitative theory of boundedness, periodicity and stability of Volterra integro-dynamic equations on time scales. Researchers and graduate students who are interested in the method of Lyapunov functions/functionals, in the study of boundedness of solutions, in the stability of the zero solution, or in the existence of periodic solutions should be able to use this book as a primary reference and as a resource of latest findings. This book contains many open problems and should be of great benefit to those who are pursuing research in dynamical systems or in Volterra integro-dynamic equations on time scales with or without delays. Great efforts were made to present rigorous and detailed proofs of theorems. The book should serve as an encyclopedia on the construction of Lyapunov functionals in analyzing solutions of dynamical systems on time scales. The book is suitable for a graduate course in the format of graduate seminars or as special topics course on dynamical systems. The book should be of interest to investigators in biology, chemistry, economics, engineering, mathematics and physics.