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Nonlinear Integral Equations On Time Scales
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Book Synopsis Nonlinear Integral Equations on Time Scales by : Svetlin G. Georgiev
Download or read book Nonlinear Integral Equations on Time Scales written by Svetlin G. Georgiev and published by . This book was released on 2019-03-26 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Integral Inequalities on Time Scales by : Svetlin G. Georgiev
Download or read book Integral Inequalities on Time Scales written by Svetlin G. Georgiev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-08-24 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Integral Equations on Time Scales by : Svetlin G. Georgiev
Download or read book Integral Equations on Time Scales written by Svetlin G. Georgiev and published by Springer. This book was released on 2016-10-30 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Integral Equations and Inclusions by : Ravi P. Agarwal
Download or read book Nonlinear Integral Equations and Inclusions written by Ravi P. Agarwal and published by Nova Publishers. This book was released on 2001 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dynamic Equations on Time Scales by : Martin Bohner
Download or read book Dynamic Equations on Time Scales written by Martin Bohner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Dynamic Inequalities On Time Scales by : Ravi Agarwal
Download or read book Dynamic Inequalities On Time Scales written by Ravi Agarwal and published by Springer. This book was released on 2014-10-30 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Boundary Value Problems on Time Scales, Volume II by : Svetlin G. Georgiev
Download or read book Boundary Value Problems on Time Scales, Volume II written by Svetlin G. Georgiev and published by CRC Press. This book was released on 2021-10-15 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary Value Problems on Time Scales, Volume II 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.
Book Synopsis Stability Theory for Dynamic Equations on Time Scales by : Anatoly A. Martynyuk
Download or read book Stability Theory for Dynamic Equations on Time Scales written by Anatoly A. Martynyuk and published by Birkhäuser. This book was released on 2016-09-22 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Advances in Dynamic Equations on Time Scales by : Martin Bohner
Download or read book Advances in Dynamic Equations on Time Scales written by Martin Bohner and published by Springer Science & Business Media. This book was released on 2002-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent introductory material on the calculus of time scales and dynamic equations.; Numerous examples and exercises illustrate the diverse application of dynamic equations on time scales.; Unified and systematic exposition of the topics allows good transitions from chapter to chapter.; Contributors include Anderson, M. Bohner, Davis, Dosly, Eloe, Erbe, Guseinov, Henderson, Hilger, Hilscher, Kaymakcalan, Lakshmikantham, Mathsen, and A. Peterson, founders and leaders of this field of study.; Useful as a comprehensive resource of time scales and dynamic equations for pure and applied mathematicians.; Comprehensive bibliography and index complete this text.
Book Synopsis Methods in Nonlinear Integral Equations by : R Precup
Download or read book Methods in Nonlinear Integral Equations written by R Precup and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods in Nonlinear Integral Equations presents several extremely fruitful methods for the analysis of systems and nonlinear integral equations. They include: fixed point methods (the Schauder and Leray-Schauder principles), variational methods (direct variational methods and mountain pass theorems), and iterative methods (the discrete continuation principle, upper and lower solutions techniques, Newton's method and the generalized quasilinearization method). Many important applications for several classes of integral equations and, in particular, for initial and boundary value problems, are presented to complement the theory. Special attention is paid to the existence and localization of solutions in bounded domains such as balls and order intervals. The presentation is essentially self-contained and leads the reader from classical concepts to current ideas and methods of nonlinear analysis.
Book Synopsis Functional Dynamic Equations on Time Scales by : Svetlin G. Georgiev
Download or read book Functional Dynamic Equations on Time Scales written by Svetlin G. Georgiev and published by Springer. This book was released on 2019-05-03 with total page 885 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations. It discusses functional dynamic equations in relation to mathematical physics applications and problems, providing useful tools for investigation for oscillations and nonoscillations of the solutions of functional dynamic equations on time scales. Practice problems are presented throughout the book for use as a graduate-level textbook and as a reference book for specialists of several disciplines, such as mathematics, physics, engineering, and biology.
Book Synopsis Conformable Dynamic Equations on Time Scales by : Douglas R. Anderson
Download or read book Conformable Dynamic Equations on Time Scales written by Douglas R. Anderson and published by CRC Press. This book was released on 2020-08-29 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Integral Equations by : Philip M. Anselone
Download or read book Nonlinear Integral Equations written by Philip M. Anselone and published by . This book was released on 1964 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Integral Equations in Abstract Spaces by : Dajun Guo
Download or read book Nonlinear Integral Equations in Abstract Spaces written by Dajun Guo and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems arising in the physical sciences, engineering, biology and ap plied mathematics lead to mathematical models described by nonlinear integral equations in abstract spaces. The theory of nonlinear integral equations in ab stract spaces is a fast growing field with important applications to a number of areas of analysis as well as other branches of science. This book is devoted to a comprehensive treatment of nonlinear integral equations in abstract spaces. It is the first book that is dedicated to a systematic development of this subject, and it includes the developments during recent years. Chapter 1 introduces some basic results in analysis, which will be used in later chapters. Chapter 2, which is a main portion of this book, deals with nonlin ear integral equations in Banach spaces, including equations of Fredholm type, of Volterra type and equations of Hammerstein type. Some applica equations tions to nonlinear differential equations in Banach spaces are given. We also discuss an integral equation modelling infectious disease as a typical applica tion. In Chapter 3, we investigate the first order and second order nonlinear integro-differential equations in Banach spaces including equations of Volterra type and equations of mixed type. Chapter 4 is devoted to nonlinear impulsive integral equations in Banach spaces and their applications to nonlinear impul sive differential equations in Banach spaces.
Book Synopsis Dynamic Calculus and Equations on Time Scales by : Svetlin G. Georgiev
Download or read book Dynamic Calculus and Equations on Time Scales written by Svetlin G. Georgiev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-09-18 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fuzzy Dynamic Equations, Dynamic Inclusions, and Optimal Control Problems on Time Scales by : Svetlin G. Georgiev
Download or read book Fuzzy Dynamic Equations, Dynamic Inclusions, and Optimal Control Problems on Time Scales written by Svetlin G. Georgiev and published by Springer Nature. This book was released on 2021-07-15 with total page 882 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of dynamic equations has many interesting applications in control theory, mathematical economics, mathematical biology, engineering and technology. In some cases, there exists uncertainty, ambiguity, or vague factors in such problems, and fuzzy theory and interval analysis are powerful tools for modeling these equations on time scales. The aim of this book is to present a systematic account of recent developments; describe the current state of the useful theory; show the essential unity achieved in the theory fuzzy dynamic equations, dynamic inclusions and optimal control problems on time scales; and initiate several new extensions to other types of fuzzy dynamic systems and dynamic inclusions. The material is presented in a highly readable, mathematically solid format. Many practical problems are illustrated, displaying a wide variety of solution techniques. The book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. Students in mathematical and physical sciences will find many sections of direct relevance.
Book Synopsis Integral Inequalities on Time Scales by : Svetlin G. Georgiev
Download or read book Integral Inequalities on Time Scales written by Svetlin G. Georgiev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-08-24 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
