Advances On Fractional Dynamic Inequalities On Time Scales

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Advances On Fractional Dynamic Inequalities On Time Scales

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Author : Svetlin G Georgiev
language : en
Publisher: World Scientific
Release Date : 2023-08-29

Advances On Fractional Dynamic Inequalities On Time Scales written by Svetlin G Georgiev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-29 with Mathematics categories.

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.

Dynamic Equations On Time Scales

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Author : Martin Bohner
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-15

Dynamic Equations On Time Scales written by Martin Bohner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-15 with Language Arts & Disciplines categories.

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

Dynamic Inequalities On Time Scales

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Author : Ravi Agarwal
language : en
Publisher: Springer
Release Date : 2014-10-30

Dynamic Inequalities On Time Scales written by Ravi Agarwal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-30 with Mathematics categories.

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.

Recent Advances In Applied Nonlinear Dynamics With Numerical Analysis Fractional Dynamics Network Dynamics Classical Dynamics And Fractal Dynamics With Their Numerical Simulations

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Author : Changpin Li
language : en
Publisher: World Scientific
Release Date : 2013-01-11

Recent Advances In Applied Nonlinear Dynamics With Numerical Analysis Fractional Dynamics Network Dynamics Classical Dynamics And Fractal Dynamics With Their Numerical Simulations written by Changpin Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-11 with Mathematics categories.

Nonlinear dynamics is still a hot and challenging topic. In this edited book, we focus on fractional dynamics, infinite dimensional dynamics defined by the partial differential equation, network dynamics, fractal dynamics, and their numerical analysis and simulation.Fractional dynamics is a new topic in the research field of nonlinear dynamics which has attracted increasing interest due to its potential applications in the real world, such as modeling memory processes and materials. In this part, basic theory for fractional differential equations and numerical simulations for these equations will be introduced and discussed.In the infinite dimensional dynamics part, we emphasize on numerical calculation and theoretical analysis, including constructing various numerical methods and computing the corresponding limit sets, etc.In the last part, we show interest in network dynamics and fractal dynamics together with numerical simulations as well as their applications.

Integral Inequalities On Time Scales

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Author : Svetlin G. Georgiev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-08-24

Integral Inequalities On Time Scales written by Svetlin G. Georgiev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-24 with Mathematics categories.

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.

Hardy Type Inequalities On Time Scales

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Author : Ravi P. Agarwal
language : en
Publisher: Springer
Release Date : 2016-10-20

Hardy Type Inequalities On Time Scales written by Ravi P. Agarwal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-20 with Mathematics categories.

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.

Frontiers In Time Scales And Inequalities

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Author : George A Anastassiou
language : en
Publisher: World Scientific
Release Date : 2015-08-06

Frontiers In Time Scales And Inequalities written by George A Anastassiou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-06 with Mathematics categories.

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.

Dynamic Equations On Time Scales And Applications

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Author : Ravi P Agarwal
language : en
Publisher: CRC Press
Release Date : 2024-10-18

Dynamic Equations On Time Scales And Applications written by Ravi P Agarwal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-18 with Mathematics categories.

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

Fractional Differential Equations Inclusions And Inequalities With Applications

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Author : Sotiris K. Ntouyas
language : en
Publisher: MDPI
Release Date : 2020-11-09

Fractional Differential Equations Inclusions And Inequalities With Applications written by Sotiris K. Ntouyas and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-09 with Mathematics categories.

During the last decade, there has been an increased interest in fractional differential equations, inclusions, and inequalities, as they play a fundamental role in the modeling of numerous phenomena, in particular, in physics, biomathematics, blood flow phenomena, ecology, environmental issues, viscoelasticity, aerodynamics, electrodynamics of complex medium, electrical circuits, electron-analytical chemistry, control theory, etc. This book presents collective works published in the recent Special Issue (SI) entitled "Fractional Differential Equation, Inclusions and Inequalities with Applications" of the journal Mathematics. This Special Issue presents recent developments in the theory of fractional differential equations and inequalities. Topics include but are not limited to the existence and uniqueness results for boundary value problems for different types of fractional differential equations, a variety of fractional inequalities, impulsive fractional differential equations, and applications in sciences and engineering.

Hadamard Type Fractional Differential Equations Inclusions And Inequalities

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Author : Bashir Ahmad
language : en
Publisher: Springer
Release Date : 2017-03-16

Hadamard Type Fractional Differential Equations Inclusions And Inequalities written by Bashir Ahmad and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-16 with Mathematics categories.

This book focuses on the recent development of fractional differential equations, integro-differential equations, and inclusions and inequalities involving the Hadamard derivative and integral. Through a comprehensive study based in part on their recent research, the authors address the issues related to initial and boundary value problems involving Hadamard type differential equations and inclusions as well as their functional counterparts. The book covers fundamental concepts of multivalued analysis and introduces a new class of mixed initial value problems involving the Hadamard derivative and Riemann-Liouville fractional integrals. In later chapters, the authors discuss nonlinear Langevin equations as well as coupled systems of Langevin equations with fractional integral conditions. Focused and thorough, this book is a useful resource for readers and researchers interested in the area of fractional calculus.