Advances On Fractional Dynamic Inequalities On Time Scales

Author : Svetlin G Georgiev
Publisher : World Scientific
ISBN 13 : 9811275483
Total Pages : 337 pages
Book Rating : 4.87/5 ( download)

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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.

Author : Ravi Agarwal
Publisher : Springer
ISBN 13 : 3319110020
Total Pages : 264 pages
Book Rating : 4.28/5 ( download)

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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.

Author : Martin Bohner
Publisher : Springer Science & Business Media
ISBN 13 : 1461202019
Total Pages : 365 pages
Book Rating : 4.11/5 ( download)

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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.

Author : Svetlin G. Georgiev
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110705664
Total Pages : 186 pages
Book Rating : 4.69/5 ( download)

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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.

Author : George A Anastassiou
Publisher : World Scientific
ISBN 13 : 9814704458
Total Pages : 289 pages
Book Rating : 4.58/5 ( download)

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Download or read book Frontiers In Time Scales And Inequalities written by George A Anastassiou and published by World Scientific. This book was released on 2015-08-06 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains the author's work of the last four years in discrete and fractional analysis. It introduces the right delta and right nabla fractional calculus on time scales and continues with the right delta and right nabla discrete fractional calculus in the Caputo sense. Then, it shows representation formulae of functions on time scales and presents Ostrowski type inequalities, Landau type inequalities, Grüss type and comparison of means inequalities, all these over time scales. The volume continues with integral operator inequalities and their multivariate vectorial versions using convexity of functions, again all these over time scales. It follows the Grüss and Ostrowski type inequalities involving s-convexity of functions; and also examines the general case when several functions are involved. Then, it presents the general fractional Hermite-Hadamard type inequalities using m-convexity and (s, m)-convexity. Finally, it introduces the reduction method in fractional calculus and its connection to fractional Ostrowski type inequalities is studied.This book's results are expected to find applications in many areas of pure and applied mathematics, especially in difference equations and fractional differential equations. The chapters are self-contained and can be read independently, and advanced courses can be taught out of it. It is suitable for researchers, graduate students, seminars of the above subjects, and serves well as an invaluable resource for all science libraries.

Author : Svetlin G. Georgiev
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111182975
Total Pages : 336 pages
Book Rating : 4.71/5 ( download)

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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.

Author : Douglas R. Anderson
Publisher : CRC Press
ISBN 13 : 100009393X
Total Pages : 347 pages
Book Rating : 4.33/5 ( download)

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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.

Author : Ravi P Agarwal
Publisher : CRC Press
ISBN 13 : 1040103758
Total Pages : 599 pages
Book Rating : 4.53/5 ( download)

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Download or read book Dynamic Equations on Time Scales and Applications written by Ravi P Agarwal and published by CRC Press. This book was released on 2024-10-18 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of dynamic equations on time scales and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results related to the qualitative properties of solutions like existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. • Presents cutting-edge research trends of dynamic equations and recent advances in contemporary research on the topic of time scales • Connects several new areas of dynamic equations on time scales with applications in different fields • Includes mathematical explanation from the perspective of existing knowledge of dynamic equations on time scales • Offers several new recently developed results, which are useful for the mathematical modeling of various phenomena • Useful for several interdisciplinary fields like economics, biology, and population dynamics from the perspective of new trends The text is for postgraduate students, professionals, and academic researchers working in the fields of Applied Mathematics

Author : Abdul-Majid Wazwaz
Publisher : World Scientific
ISBN 13 : 9789810231019
Total Pages : 228 pages
Book Rating : 4.16/5 ( download)

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Download or read book A First Course in Integral Equations written by Abdul-Majid Wazwaz and published by World Scientific. This book was released on 1997 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the subject of integral equations in an accessible manner for a variety of applications. Emphasis is placed on understanding the subject while avoiding the abstract and compact theorems. A distinctive feature of the book is that it introduces the recent powerful and reliable developments in this field, which are not covered in traditional texts. The newly developed decomposition method, the series solution method and the direct computation method are thoroughly implemented, which allows the topic to be far more accessible. The book also includes some of the traditional techniques for comparison.Using the newly developed methods, the author successfully handles Fredholm and Volterra integral equations, singular integral equations, integro-differential equations and nonlinear integral equations, with promising results for linear and nonlinear models. Many examples are given to introduce the material in a clear and thorough fashion. In addition, many exercises are provided to build confidence, ease and skill in using the new methods.This book may be used as a text for advanced undergraduates and graduate students in mathematics and scientific areas, and as a work of reference for research study of differential equations and numerical analysis.

Author : Ravi P. Agarwal
Publisher : Springer
ISBN 13 : 3319442996
Total Pages : 309 pages
Book Rating : 4.90/5 ( download)

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Download or read book Hardy Type Inequalities on Time Scales written by Ravi P. Agarwal and published by Springer. This book was released on 2016-10-20 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to dynamic inequalities of Hardy type and extensions and generalizations via convexity on a time scale T. In particular, the book contains the time scale versions of classical Hardy type inequalities, Hardy and Littlewood type inequalities, Hardy-Knopp type inequalities via convexity, Copson type inequalities, Copson-Beesack type inequalities, Liendeler type inequalities, Levinson type inequalities and Pachpatte type inequalities, Bennett type inequalities, Chan type inequalities, and Hardy type inequalities with two different weight functions. These dynamic inequalities contain the classical continuous and discrete inequalities as special cases when T = R and T = N and can be extended to different types of inequalities on different time scales such as T = hN, h > 0, T = qN for q > 1, etc.In this book the authors followed the history and development of these inequalities. Each section in self-contained and one can see the relationship between the time scale versions of the inequalities and the classical ones. To the best of the authors’ knowledge this is the first book devoted to Hardy-typeinequalities and their extensions on time scales.