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Multivariable Dynamic Calculus On Time Scales
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Book Synopsis Multivariable Dynamic Calculus on Time Scales by : Martin Bohner
Download or read book Multivariable Dynamic Calculus on Time Scales written by Martin Bohner and published by Springer. This book was released on 2017-03-20 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers the reader an overview of recent developments of multivariable dynamic calculus on time scales, taking readers beyond the traditional calculus texts. Covering topics from parameter-dependent integrals to partial differentiation on time scales, the book’s nine pedagogically oriented chapters provide a pathway to this active area of research that will appeal to students and researchers in mathematics and the physical sciences. The authors present a clear and well-organized treatment of the concept behind the mathematics and solution techniques, including many practical examples and exercises.
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 348 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 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 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 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales by : Svetlin G. Georgiev
Download or read book Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales written by Svetlin G. Georgiev and published by Springer. This book was released on 2018-04-12 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided for solving differential and integral equations as well as various problems involving special functions of mathematical physics and their extensions and generalizations in one and more variables. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations. Intended for use in the field and designed for students without an extensive mathematical background, this book is suitable for graduate courses and researchers looking for an introduction to fractional dynamic calculus and equations on time scales.
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 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 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.
Book Synopsis Numerical Analysis on Time Scales by : Svetlin G. Georgiev
Download or read book Numerical Analysis on Time Scales written by Svetlin G. Georgiev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-09-05 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models cannot be solved using the traditional analytical methods for dynamic equations on time scales. These models must be dealt with using computational methods. This textbook introduces numerical methods for initial value problems for dynamic equations on time scales. Hands-on examples utilizing MATLAB and practical problems illustrate a wide variety of solution techniques.
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.
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 de Gruyter. This book was released on 2020 with total page 0 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 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 Recent Trends in Fractional Calculus and Its Applications by : Praveen Agarwal
Download or read book Recent Trends in Fractional Calculus and Its Applications written by Praveen Agarwal and published by Elsevier. This book was released on 2024-07-19 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent Trends in Fractional Calculus and Its Applications addresses the answer to this very basic question: "Why is Fractional Calculus important?" Until recent times, Fractional Calculus was considered as a rather esoteric mathematical theory without applications, but in the last few decades there has been an explosion of research activities on the application of Fractional Calculus to very diverse scientific fields ranging from the physics of diffusion and advection phenomena, to control systems to finance and economics. An important part of mathematical modelling of objects and processes is a description of their dynamics. The term Fractional Calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to noninteger (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. Several mathematicians contributed to this subject over the years. People like Liouville, Riemann, and Weyl made major contributions to the theory of Fractional Calculus. In recent decades the field of Fractional Calculus has attracted the interest of researchers in several areas, including mathematics, physics, chemistry, engineering, finance, and social sciences. Provides the most recent and up-to-date developments in the Fractional Calculus and its application areas Presents pre-preparation ideas to help researchers/scientists/clinicians face the new challenges in the application of fractional differential equations Helps researchers and scientists understand the importance of the Fractional Calculus to solve many problems in Biomedical Engineering and applied sciences
Book Synopsis Advances in Differential and Difference Equations with Applications 2020 by : Dumitru Baleanu
Download or read book Advances in Differential and Difference Equations with Applications 2020 written by Dumitru Baleanu and published by MDPI. This book was released on 2021-01-20 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is very well known that differential equations are related with the rise of physical science in the last several decades and they are used successfully for models of real-world problems in a variety of fields from several disciplines. Additionally, difference equations represent the discrete analogues of differential equations. These types of equations started to be used intensively during the last several years for their multiple applications, particularly in complex chaotic behavior. A certain class of differential and related difference equations is represented by their respective fractional forms, which have been utilized to better describe non-local phenomena appearing in all branches of science and engineering. The purpose of this book is to present some common results given by mathematicians together with physicists, engineers, as well as other scientists, for whom differential and difference equations are valuable research tools. The reported results can be used by researchers and academics working in both pure and applied differential equations.
Book Synopsis Difference Equations, Discrete Dynamical Systems and Applications by : Sorin Olaru
Download or read book Difference Equations, Discrete Dynamical Systems and Applications written by Sorin Olaru and published by Springer Nature. This book was released on with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lyapunov Inequalities and Applications by : Ravi P. Agarwal
Download or read book Lyapunov Inequalities and Applications written by Ravi P. Agarwal and published by Springer Nature. This book was released on 2021-04-12 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive survey on Lyapunov-type inequalities. It summarizes and puts order into a vast literature available on the subject, and sketches recent developments in this topic. In an elegant and didactic way, this work presents the concepts underlying Lyapunov-type inequalities, covering how they developed and what kind of problems they address. This survey starts by introducing basic applications of Lyapunov’s inequalities. It then advances towards even-order, odd-order, and higher-order boundary value problems; Lyapunov and Hartman-type inequalities; systems of linear, nonlinear, and quasi-linear differential equations; recent developments in Lyapunov-type inequalities; partial differential equations; linear difference equations; and Lyapunov-type inequalities for linear, half-linear, and nonlinear dynamic equations on time scales, as well as linear Hamiltonian dynamic systems. Senior undergraduate students and graduate students of mathematics, engineering, and science will benefit most from this book, as well as researchers in the areas of ordinary differential equations, partial differential equations, difference equations, and dynamic equations. Some background in calculus, ordinary and partial differential equations, and difference equations is recommended for full enjoyment of the content.
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.
