Fuzzy Dynamic Equations Dynamic Inclusions And Optimal Control Problems On Time Scales

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Fuzzy Dynamic Equations, Dynamic Inclusions, and Optimal Control Problems on Time Scales

Author : Svetlin G. Georgiev
Publisher : Springer Nature
ISBN 13 : 3030761320
Total Pages : 882 pages
Book Rating : 4.0/5 (37 download)

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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.

Boundary Value Problems

Author : Svetlin Georgiev
Publisher :
ISBN 13 : 9783031382024
Total Pages : 0 pages
Book Rating : 4.3/5 (82 download)

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Book Synopsis Boundary Value Problems by : Svetlin Georgiev

Download or read book Boundary Value Problems written by Svetlin Georgiev and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Boundary Value Problems

Author : Svetlin Georgiev
Publisher : Springer Nature
ISBN 13 : 3031381963
Total Pages : 171 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Boundary Value Problems by : Svetlin Georgiev

Download or read book Boundary Value Problems written by Svetlin Georgiev and published by Springer Nature. This book was released on 2023-08-16 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

First Order Partial Dynamic Equations on Time Scales

Author : Svetlin G. Georgiev
Publisher : Cambridge Scholars Publishing
ISBN 13 : 1036401952
Total Pages : 377 pages
Book Rating : 4.0/5 (364 download)

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Book Synopsis First Order Partial Dynamic Equations on Time Scales by : Svetlin G. Georgiev

Download or read book First Order Partial Dynamic Equations on Time Scales written by Svetlin G. Georgiev and published by Cambridge Scholars Publishing. This book was released on 2024-03-05 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advances On Fractional Dynamic Inequalities On Time Scales

Author : Svetlin G Georgiev
Publisher : World Scientific
ISBN 13 : 9811275483
Total Pages : 337 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Advances On Fractional Dynamic Inequalities On Time Scales by : Svetlin G Georgiev

Download or read book Advances On Fractional Dynamic Inequalities On Time Scales written by Svetlin G Georgiev and published by World Scientific. This book was released on 2023-08-29 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

First Order Partial Dynamic Equations on Time Scales

Author : Svetlin G. Georgiev
Publisher :
ISBN 13 : 9781036401948
Total Pages : 0 pages
Book Rating : 4.4/5 (19 download)

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Book Synopsis First Order Partial Dynamic Equations on Time Scales by : Svetlin G. Georgiev

Download or read book First Order Partial Dynamic Equations on Time Scales written by Svetlin G. Georgiev and published by . This book was released on 2024-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dynamic Equations and Almost Periodic Fuzzy Functions on Time Scales

Author : Chao Wang
Publisher : Springer Nature
ISBN 13 : 3031112369
Total Pages : 195 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Dynamic Equations and Almost Periodic Fuzzy Functions on Time Scales by : Chao Wang

Download or read book Dynamic Equations and Almost Periodic Fuzzy Functions on Time Scales written by Chao Wang and published by Springer Nature. This book was released on 2022-09-20 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Metrical Almost Periodicity and Applications to Integro-Differential Equations

Author : Marko Kostić
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111233871
Total Pages : 576 pages
Book Rating : 4.1/5 (112 download)

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Book Synopsis Metrical Almost Periodicity and Applications to Integro-Differential Equations by : Marko Kostić

Download or read book Metrical Almost Periodicity and Applications to Integro-Differential Equations written by Marko Kostić and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-06-06 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dynamic Equations on Time Scales

Author : Martin Bohner
Publisher : Springer Science & Business Media
ISBN 13 : 9780817642259
Total Pages : 460 pages
Book Rating : 4.6/5 (422 download)

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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 2001-06-15 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

An Excursion Through Partial Differential Equations

Author : Svetlin G. Georgiev
Publisher : Springer Nature
ISBN 13 : 3031487842
Total Pages : 424 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis An Excursion Through Partial Differential Equations by : Svetlin G. Georgiev

Download or read book An Excursion Through Partial Differential Equations written by Svetlin G. Georgiev and published by Springer Nature. This book was released on 2024-01-17 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Set Dynamic Equations on Time Scales: A Brief Introduction with Applications

Author : Shihuang Hong
Publisher : World Scientific Publishing Company
ISBN 13 : 9789811296406
Total Pages : 0 pages
Book Rating : 4.2/5 (964 download)

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Book Synopsis Set Dynamic Equations on Time Scales: A Brief Introduction with Applications by : Shihuang Hong

Download or read book Set Dynamic Equations on Time Scales: A Brief Introduction with Applications written by Shihuang Hong and published by World Scientific Publishing Company. This book was released on 2025-02-02 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The process of authoring this book is inspired by the recent increased activity of research on dynamic equations on time scales and other closely related areas. This monograph is the first published book that attempts to provide a comprehensive view of the theory and applications of set dynamic equations on time scales. The main focus of the book is the qualitative theory of set dynamic equations and their applications to fuzzy dynamic equations. The key topics include the solvability of set dynamic equations, stability of set dynamic equations, and applications to certain types of fuzzy dynamic equations.There are five chapters in the book, through which the authors examine a wide scope of the concept of set dynamic equations and their applications. Each chapter focuses on theory and proofs to enrich the reader's understanding of the topic.This book will be particularly useful to those experts who work in applied analysis, in general. It will also be a good reference for computer scientists since it covers fuzzy dynamic equations. Researchers and graduate students at various levels interested in learning about set dynamic equations and related fields will find this text a valuable resource of both introductory and advanced material.

Advances in Dynamic Equations on Time Scales

Author : Martin Bohner
Publisher : Springer Science & Business Media
ISBN 13 : 0817682309
Total Pages : 354 pages
Book Rating : 4.8/5 (176 download)

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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 2011-06-28 with total page 354 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.

Functional Dynamic Equations on Time Scales

Author : Svetlin G. Georgiev
Publisher : Springer
ISBN 13 : 3030154203
Total Pages : 885 pages
Book Rating : 4.0/5 (31 download)

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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.

Interval Analysis

Author : Navid Razmjooy
Publisher : John Wiley & Sons
ISBN 13 : 1394190999
Total Pages : 212 pages
Book Rating : 4.3/5 (941 download)

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Book Synopsis Interval Analysis by : Navid Razmjooy

Download or read book Interval Analysis written by Navid Razmjooy and published by John Wiley & Sons. This book was released on 2023-12-04 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interval Analysis An innovative and unique application of interval analysis to optimal control problems In Interval Analysis: Application in the Optimal Control Problems, celebrated researcher and engineer Dr. Navid Razmjooy delivers an expert discussion of the uncertainties in the analysis of optimal control problems. In the book, Dr. Razmjooy uses an open-ended approach to solving optimal control problems with indefinite intervals. Utilizing an extended, Runge-Kutta method, the author demonstrates how to accelerate its speed with the piecewise function. You’ll find recursive methods used to achieve more compact answers, as well as how to solve optimal control problems using the interval Chebyshev’s function. The book also contains: A thorough introduction to common errors and mistakes, generating uncertainties in physical models Comprehensive explorations of the literature on the subject, including Hukurara’s derivatives Practical discussions of the interval analysis and its variants, including the classical (Minkowski) methods Complete treatments of existing control methods, including classic, conventional advanced, and robust control. Perfect for master’s and PhD students working on system uncertainties, Interval Analysis: Application in the Optimal Control Problems will also benefit researchers working in laboratories, universities, and research centers.

Jordan Canonical Form and Dynamic Systems on Time Scales

Author : SVETLIN G. GEORGIEV
Publisher :
ISBN 13 : 9781527594760
Total Pages : 0 pages
Book Rating : 4.5/5 (947 download)

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Book Synopsis Jordan Canonical Form and Dynamic Systems on Time Scales by : SVETLIN G. GEORGIEV

Download or read book Jordan Canonical Form and Dynamic Systems on Time Scales written by SVETLIN G. GEORGIEV and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Extremal Fuzzy Dynamic Systems

Author : Gia Sirbiladze
Publisher : Springer Science & Business Media
ISBN 13 : 1461442508
Total Pages : 416 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Extremal Fuzzy Dynamic Systems by : Gia Sirbiladze

Download or read book Extremal Fuzzy Dynamic Systems written by Gia Sirbiladze and published by Springer Science & Business Media. This book was released on 2012-09-25 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author presents a new approach to the study of weakly structurable dynamic systems. It differs from other approaches by considering time as a source of fuzzy uncertainty in dynamic systems. It begins with a thorough introduction, where the general research domain, the problems, and ways of their solutions are discussed. The book then progresses systematically by first covering the theoretical aspects before tackling the applications. In the application section, a software library is described, which contains discrete EFDS identification methods elaborated during fundamental research of the book. Extremal Fuzzy Dynamic Systems will be of interest to theoreticians interested in modeling fuzzy processes, to researchers who use fuzzy statistics, as well as practitioners from different disciplines whose research interests include abnormal, extreme and monotone processes in nature and society. Graduate students could also find this book useful.

Stability Theory for Dynamic Equations on Time Scales

Author : Anatoly A. Martynyuk
Publisher : Birkhäuser
ISBN 13 : 9783319825267
Total Pages : 223 pages
Book Rating : 4.8/5 (252 download)

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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 2018-04-22 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.