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Author: Svetlin G. Georgiev
Publisher:
ISBN: 9781536150216
Category :
Languages : en
Pages : 356
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Book Description
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.
Author: Svetlin G. Georgiev
Publisher:
ISBN: 9781536150216
Category :
Languages : en
Pages : 356
Get Book Here
Book Description
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.
Author: Svetlin G. Georgiev
Publisher: Springer
ISBN: 9462392285
Category : Mathematics
Languages : en
Pages : 403
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Book Description
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.
Author: Svetlin G. Georgiev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110705559
Category : Mathematics
Languages : en
Pages : 316
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Book Description
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.
Author: Martin Bohner
Publisher: Springer Science & Business Media
ISBN: 1461202019
Category : Mathematics
Languages : en
Pages : 365
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Book Description
On becoming familiar with difference equations and their close re lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals.
Author: Douglas R. Anderson
Publisher: CRC Press
ISBN: 100009393X
Category : Mathematics
Languages : en
Pages : 347
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Book Description
The concept of derivatives of non-integer order, known as fractional derivatives, first appeared in the letter between L’Hopital and Leibniz in which the question of a half-order derivative was posed. Since then, many formulations of fractional derivatives have appeared. Recently, a new definition of fractional derivative, called the "fractional conformable derivative," has been introduced. This new fractional derivative is compatible with the classical derivative and it has attracted attention in areas as diverse as mechanics, electronics, and anomalous diffusion. Conformable Dynamic Equations on Time Scales is devoted to the qualitative theory of conformable dynamic equations on time scales. This book summarizes the most recent contributions in this area, and vastly expands on them to conceive of a comprehensive theory developed exclusively for this book. Except for a few sections in Chapter 1, the results here are presented for the first time. As a result, the book is intended for researchers who work on dynamic calculus on time scales and its applications. Features Can be used as a textbook at the graduate level as well as a reference book for several disciplines Suitable for an audience of specialists such as mathematicians, physicists, engineers, and biologists Contains a new definition of fractional derivative About the Authors Douglas R. Anderson is professor and chair of the mathematics department at Concordia College, Moorhead. His research areas of interest include dynamic equations on time scales and Ulam-type stability of difference and dynamic equations. He is also active in investigating the existence of solutions for boundary value problems. Svetlin G. Georgiev is currently professor at Sorbonne University, Paris, France and works in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, dynamic calculus on time scales, and integral equations.
Author: Anatoly A. Martynyuk
Publisher: Birkhäuser
ISBN: 3319422138
Category : Mathematics
Languages : en
Pages : 233
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Book Description
This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems.In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Mathematics,” 1937, E.T.Bell wrote: “A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both.”Mathematical analysis on time scales accomplishes exactly this. This research has potential applications in such areas as theoretical and applied mechanics, neurodynamics, mathematical biology and finance among others.
Author: Ravi Agarwal
Publisher: Springer
ISBN: 3319110020
Category : Mathematics
Languages : en
Pages : 264
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Book Description
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.
Author: Svetlin G. Georgiev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111185192
Category : Mathematics
Languages : en
Pages : 370
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Book Description
Author: Matiur Rahman
Publisher: WIT Press
ISBN: 1845641019
Category : Mathematics
Languages : en
Pages : 385
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Book Description
The book deals with linear integral equations, that is, equations involving an unknown function which appears under the integral sign and contains topics such as Abel's integral equation, Volterra integral equations, Fredholm integral integral equations, singular and nonlinear integral equations, orthogonal systems of functions, Green's function as a symmetric kernel of the integral equations.
Author:
Publisher: Elsevier
ISBN: 0080534643
Category : Mathematics
Languages : en
Pages : 623
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Book Description
Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books. Written by a major contributor to the field, this comprehensive resource contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools in the development of applications in the theory of new classes of differential and integral equations. For researchers working in this area, it will be a valuable source of reference and inspiration. It could also be used as the text for an advanced graduate course. - Covers a variety of linear and nonlinear inequalities which find widespread applications in the theory of various classes of differential and integral equations - Contains many inequalities which have only recently appeared in literature and cannot yet be found in other books - Provides a valuable reference to engineers and graduate students
