Fuzzy Dynamic Equations, Dynamic Inclusions, and Optimal Control Problems on Time Scales PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Fuzzy Dynamic Equations, Dynamic Inclusions, and Optimal Control Problems on Time Scales PDF full book. Access full book title Fuzzy Dynamic Equations, Dynamic Inclusions, and Optimal Control Problems on Time Scales by Svetlin G. Georgiev. Download full books in PDF and EPUB format.
Author: Svetlin G. Georgiev
Publisher: Springer Nature
ISBN: 3030761320
Category : Mathematics
Languages : en
Pages : 882
Get Book Here
Book Description
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.
Author: Svetlin G. Georgiev
Publisher: Springer Nature
ISBN: 3030761320
Category : Mathematics
Languages : en
Pages : 882
Get Book Here
Book Description
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.
Author: Svetlin Georgiev
Publisher:
ISBN: 9783031382024
Category : Differential equations
Languages : en
Pages : 0
Get Book Here
Book Description
This book explores boundary value problems for fractional dynamic equations on arbitrary time scales, including Caputo fractional dynamic equations, impulsive Caputo fractional dynamic equations, and impulsive Riemann-Liouville fractional dynamic equations. The author provides an introduction to each fractional dynamic equation before delving into the problems. The book also covers initial value problems, boundary value problems, initial boundary value problems for each type of equation. The author provides integral representations of the solutions and proves the existence and uniqueness of the solutions. In addition, this book: Explains the topic for a wide audience including physicists, engineers, biologists, and students of various disciplines Explores boundary value problems for advanced fractional dynamic equations on arbitrary time scales Presents a solution technique applicable to other problems for fractional dynamic equations on arbitrary time scales About the Author: Svetlin Georgiev, Ph.D., is an Assistant Professor in the Faculty of Mathematics and Informatics at Sofia University. He was previously affiliated with Sorbonne University. He is the author of several books, including Real Quaternion Calculus Handbook, Theory of Distributions, Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales, Fuzzy Dynamic Equations, Dynamic Inclusions and Optimal Control Problems on Time Scales, and Functional Dynamic Equations on Time Scales, published by Springer Nature. His current research interests include harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales.
Author: Svetlin G. Georgiev
Publisher: Cambridge Scholars Publishing
ISBN: 1036401952
Category : Mathematics
Languages : en
Pages : 377
Get Book Here
Book Description
This book presents an introduction to the theory of first order partial dynamic equations (PDEs) on time scales. The book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses, but students in mathematical and physical sciences will also find many sections relevant. This book contains five chapters, and each chapter consists of results with their proofs, numerous examples, and exercises with solutions. Each chapter concludes with a section featuring advanced practical problems with solutions followed by a section on notes and references, explaining its context within existing literature. The book presents a clear and well-organized treatment of the concept behind the development of mathematics as well as solution techniques, and the text of this book is presented in a readable and mathematically solid format.
Author: Svetlin Georgiev
Publisher:
ISBN: 9783031381980
Category : Differential equations
Languages : en
Pages : 0
Get Book Here
Book Description
This book explores boundary value problems for Riemann-Liouville fractional dynamic equations on arbitrary time scales as well as the shifting problem on the whole time scale. The author includes an introductory overview of fractional dynamic calculus on time scales. The book also introduces the Laplace transform on arbitrary time scales, including the bilateral Laplace transform, the Laplace transform of power series, and a deduction of an inverse formula. The author then discusses the generalized convolutions of functions on arbitrary time scales and the shifting problem for existence of solutions. The book moves on to cover boundary value problems and initial boundary value problems for some classes Riemann-Liouville fractional dynamic equations. In addition, this book: Explains the topic for a wide audience including physicists, engineers, biologists, and students of various disciplines Presents a solution technique applicable to other problems for fractional dynamic equations on arbitrary time scales Provides an introduction to boundary value problems for fractional dynamic equations on arbitrary time scales.
Author: Svetlin G Georgiev
Publisher: World Scientific
ISBN: 9811275483
Category : Mathematics
Languages : en
Pages : 337
Get Book Here
Book Description
This book is devoted on recent developments of linear and nonlinear fractional Riemann-Liouville and Caputo integral inequalities on time scales. The book is intended for the use in the field of fractional dynamic calculus on time scales and fractional dynamic equations on time scales. It is also suitable for graduate courses in the above fields, and contains ten chapters. The aim of this book is to present a clear and well-organized treatment of the concept behind the development of mathematics as well as solution techniques. The text material of this book is presented in a readable and mathematically solid format.
Author: Svetlin G. Georgiev
Publisher:
ISBN: 9781036401948
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
This book presents an introduction to the theory of first order partial dynamic equations (PDEs) on time scales. The book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses, but students in mathematical and physical sciences will also find many sections relevant. This book contains five chapters, and each chapter consists of results with their proofs, numerous examples, and exercises with solutions. Each chapter concludes with a section featuring advanced practical problems with solutions followed by a section on notes and references, explaining its context within existing literature. The book presents a clear and well-organized treatment of the concept behind the development of mathematics as well as solution techniques, and the text of this book is presented in a readable and mathematically solid format.
Author: Chao Wang
Publisher: Springer Nature
ISBN: 3031112369
Category : Mathematics
Languages : en
Pages : 195
Get Book Here
Book Description
This book systematically establishes the almost periodic theory of dynamic equations and presents applications on time scales in fuzzy mathematics and uncertainty theory. The authors introduce a new division of fuzzy vectors depending on a determinant algorithm and develop a theory of almost periodic fuzzy multidimensional dynamic systems on time scales. Several applications are studied; in particular, a new type of fuzzy dynamic systems called fuzzy q-dynamic systems (i.e. fuzzy quantum dynamic systems) is presented. The results are not only effective on classical fuzzy dynamic systems, including their continuous and discrete situations, but are also valid for other fuzzy multidimensional dynamic systems on various hybrid domains. In an effort to achieve more accurate analysis in real world applications, the authors propose a number of uncertain factors in the theory. As such, fuzzy dynamical models, interval-valued functions, differential equations, fuzzy-valued differential equations, and their applications to dynamic equations on time scales are considered.
Author: Marko Kostić
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111233871
Category : Mathematics
Languages : en
Pages : 576
Get Book Here
Book Description
Author: Martin Bohner
Publisher: Springer Science & Business Media
ISBN: 9780817642259
Category : Language Arts & Disciplines
Languages : en
Pages : 460
Get Book Here
Book Description
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
Author: Svetlin G. Georgiev
Publisher: Springer Nature
ISBN: 3031487842
Category : Mathematics
Languages : en
Pages : 424
Get Book Here
Book Description
Presenting a rich collection of exercises on partial differential equations, this textbook equips readers with 96 examples, 222 exercises, and 289 problems complete with detailed solutions or hints. It explores a broad spectrum of partial differential equations, fundamental to mathematically oriented scientific fields, from physics and engineering to differential geometry and variational calculus. Organized thoughtfully into seven chapters, the journey begins with fundamental problems in the realm of PDEs. Readers progress through first and second-order equations, wave and heat equations, and finally, the Laplace equation. The text adopts a highly readable and mathematically solid format, ensuring concepts are introduced with clarity and organization. Designed to cater to upper undergraduate and graduate students, this book offers a comprehensive understanding of partial differential equations. Researchers and practitioners seeking to strengthen their problem-solving skills will also find this exercise collection both challenging and beneficial.
