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Fractional Differentiation Inequalities
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Author :George A. Anastassiou Publisher :Springer Science & Business Media ISBN 13 :0387981284 Total Pages :672 pages Book Rating :4.3/5 (879 download)
Book Synopsis Fractional Differentiation Inequalities by : George A. Anastassiou
Download or read book Fractional Differentiation Inequalities written by George A. Anastassiou and published by Springer Science & Business Media. This book was released on 2009-05-28 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author presents the Opial, Poincaré, Sobolev, Hilbert, and Ostrowski fractional differentiation inequalities. Results for the above are derived using three different types of fractional derivatives, namely by Canavati, Riemann-Liouville and Caputo. The univariate and multivariate cases are both examined. Each chapter is self-contained. The theory is presented systematically along with the applications. The application to information theory is also examined. This monograph is suitable for researchers and graduate students in pure mathematics. Applied mathematicians, engineers, and other applied scientists will also find this book useful.
Author :George A. Anastassiou Publisher :Springer Science & Business Media ISBN 13 :1461407036 Total Pages :123 pages Book Rating :4.4/5 (614 download)
Book Synopsis Advances on Fractional Inequalities by : George A. Anastassiou
Download or read book Advances on Fractional Inequalities written by George A. Anastassiou and published by Springer Science & Business Media. This book was released on 2011-07-25 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances on Fractional Inequalities use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which involves the balanced fractional derivatives. The book continues with right and mixed fractional differentiation Ostrowski inequalities in the univariate and multivariate cases. Next the right and left, as well as mixed, Landau fractional differentiation inequalities in the univariate and multivariate cases are illustrated. Throughout the book many applications are given. Fractional differentiation inequalities are by themselves an important and great mathematical topic for research. Furthermore they have many applications, the most important ones are in establishing uniqueness of solution in fractional differential equations and systems and in fractional partial differential equations. Also they provide upper bounds to the solutions of the above equations. Fractional Calculus has emerged as very useful over the last forty years due to its many applications in almost all applied sciences. This is currently seen in applications in acoustic wave propagation in inhomogeneous porous material, diffusive transport, fluid flow, dynamical processes in self-similar structures, dynamics of earthquakes, optics, geology, viscoelastic materials, bio-sciences, bioengineering, medicine, economics, probability and statistics, astrophysics, chemical engineering, physics, splines, tomography, fluid mechanics, electromagnetic waves, nonlinear control, signal processing, control of power electronic, converters, chaotic dynamics, polymer science, proteins, polymer physics, electrochemistry, statistical physics, rheology, thermodynamics, neural networks, etc. Almost all fields of research in science and engineering use fractional calculus in order to describe results. This book is a part of Fractional Calculus, therefore it is useful for researchers and graduate students for research, seminars and advanced graduate courses, in pure and applied mathematics, engineering and all other applied sciences.
Book Synopsis Generalized Fractional Calculus by : George A. Anastassiou
Download or read book Generalized Fractional Calculus written by George A. Anastassiou and published by Springer Nature. This book was released on 2020-11-25 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book applies generalized fractional differentiation techniques of Caputo, Canavati and Conformable types to a great variety of integral inequalities e.g. of Ostrowski and Opial types, etc. Some of these are extended to Banach space valued functions. These inequalities have also great impact in numerical analysis, stochastics and fractional differential equations. The book continues with generalized fractional approximations by positive sublinear operators which derive from the presented Korovkin type inequalities and also includes abstract cases. It presents also multivariate complex Korovkin quantitative approximation theory. It follows M-fractional integral inequalities of Ostrowski and Polya types. The results are weighted so they provide a great variety of cases and applications. The second part of the book deals with the quantitative fractional Korovkin type approximation of stochastic processes and lays there the foundations of stochastic fractional calculus. The book considers both Caputo and Conformable fractional directions and derives regular and trigonometric results. The positive linear operators can be expectation operator commutative or not. This book results are expected to find applications in many areas of pure and applied mathematics and stochastics. As such this monograph is suitable for researchers, graduate students, and seminars of the above disciplines, also to be in all science and engineering libraries.
Book Synopsis Constructive Fractional Analysis with Applications by : George A. Anastassiou
Download or read book Constructive Fractional Analysis with Applications written by George A. Anastassiou and published by Springer Nature. This book was released on 2021-04-01 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes constructive approximation theory; it presents ordinary and fractional approximations by positive sublinear operators, and high order approximation by multivariate generalized Picard, Gauss–Weierstrass, Poisson–Cauchy and trigonometric singular integrals. Constructive and Computational Fractional Analysis recently is more and more in the center of mathematics because of their great applications in the real world. In this book, all presented is original work by the author given at a very general level to cover a maximum number of cases in various applications. The author applies generalized fractional differentiation techniques of Riemann–Liouville, Caputo and Canavati types and of fractional variable order to various kinds of inequalities such as of Opial, Hardy, Hilbert–Pachpatte and on the spherical shell. He continues with E. R. Love left- and right-side fractional integral inequalities. They follow fractional Landau inequalities, of left and right sides, univariate and multivariate, including ones for Semigroups. These are developed to all possible directions, and right-side multivariate fractional Taylor formulae are proven for the purpose. It continues with several Gronwall fractional inequalities of variable order. This book results are expected to find applications in many areas of pure and applied mathematics. As such this book is suitable for researchers, graduate students and seminars of the above disciplines, also to be in all science and engineering libraries.
Book Synopsis Intelligent Analysis: Fractional Inequalities and Approximations Expanded by : George A. Anastassiou
Download or read book Intelligent Analysis: Fractional Inequalities and Approximations Expanded written by George A. Anastassiou and published by Springer Nature. This book was released on 2020-01-15 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on computational and fractional analysis, two areas that are very important in their own right, and which are used in a broad variety of real-world applications. We start with the important Iyengar type inequalities and we continue with Choquet integral analytical inequalities, which are involved in major applications in economics. In turn, we address the local fractional derivatives of Riemann–Liouville type and related results including inequalities. We examine the case of low order Riemann–Liouville fractional derivatives and inequalities without initial conditions, together with related approximations. In the next section, we discuss quantitative complex approximation theory by operators and various important complex fractional inequalities. We also cover the conformable fractional approximation of Csiszar’s well-known f-divergence, and present conformable fractional self-adjoint operator inequalities. We continue by investigating new local fractional M-derivatives that share all the basic properties of ordinary derivatives. In closing, we discuss the new complex multivariate Taylor formula with integral remainder. Sharing results that can be applied in various areas of pure and applied mathematics, the book offers a valuable resource for researchers and graduate students, and can be used to support seminars in related fields.
Book Synopsis Theory and Applications of Fractional Differential Equations by : A.A. Kilbas
Download or read book Theory and Applications of Fractional Differential Equations written by A.A. Kilbas and published by Elsevier. This book was released on 2006-02-16 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.
Book Synopsis Unification of Fractional Calculi with Applications by : George A. Anastassiou
Download or read book Unification of Fractional Calculi with Applications written by George A. Anastassiou and published by Springer Nature. This book was released on 2021-11-21 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates the unifying methods of generalized versions of Hilfer, Prabhakar and Hilfer–Prabhakar fractional calculi, and we establish related unifying fractional integral inequalities of the following types: Iyengar, Landau, Polya, Ostrowski, Hilbert–Pachpatte, Hardy, Opial, Csiszar’s f-Divergence, self-adjoint operator and related to fuzziness. Our results are univariate and multivariate. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional inequalities and fractional differential equations. Other interesting applications can be in applied sciences like geophysics, physics, chemistry, economics and engineering. This book is appropriate for researchers, graduate students, practitioners and seminars of the above disciplines, also to be in all science and engineering libraries.
Book Synopsis Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations by : George A. Anastassiou
Download or read book Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations written by George A. Anastassiou and published by Springer. This book was released on 2017-09-02 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief book presents the strong fractional analysis of Banach space valued functions of a real domain. The book’s results are abstract in nature: analytic inequalities, Korovkin approximation of functions and neural network approximation. The chapters are self-contained and can be read independently. This concise book is suitable for use in related graduate classes and many research projects. An extensive list of references is provided for each chapter. The book’s results are relevant for many areas of pure and applied mathematics. As such, it offers a unique resource for researchers, and a valuable addition to all science and engineering libraries.
Book Synopsis Fractional Hermite-Hadamard Inequalities by : JinRong Wang
Download or read book Fractional Hermite-Hadamard Inequalities written by JinRong Wang and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-05-22 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book extends classical Hermite-Hadamard type inequalities to the fractional case via establishing fractional integral identities, and discusses Riemann-Liouville and Hadamard integrals, respectively, by various convex functions. Illustrating theoretical results via applications in special means of real numbers, it is an essential reference for applied mathematicians and engineers working with fractional calculus. Contents Introduction Preliminaries Fractional integral identities Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals Hermite-Hadamard inequalities involving Hadamard fractional integrals
Book Synopsis Fractional Differential Equations by : Zhi-Zhong Sun
Download or read book Fractional Differential Equations written by Zhi-Zhong Sun and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-08-24 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with an introduction to fractional derivatives and numerical approximations, this book presents finite difference methods for fractional differential equations, including time-fractional sub-diffusion equations, time-fractional wave equations, and space-fractional differential equations, among others. Approximation methods for fractional derivatives are developed and approximate accuracies are analyzed in detail.
Book Synopsis Frontiers in Time Scales and Inequalities by : George A Anastassiou
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 288 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. Contents:Foundations of Right Delta Fractional Calculus on Time ScalesPrinciples of Right Nabla Fractional Calculus on Time ScalesAbout Right Delta Discrete FractionalityAbout Right Nabla Discrete Fractional CalculusRepresentations and Ostrowski Inequalities over Time ScalesLandau Inequalities on Time ScalesGrüss and Comparison of Means Inequalities over Time ScalesAbout Integral Operator Inequalities over Time ScalesAbout Vectorial Integral Operator Inequalities Using Convexity over Time ScalesGeneral Grüss and Ostrowski Inequalities Using s-ConvexityEssential and s-Convexity Ostrowski and Grüss Inequalities Using Several FunctionsGeneral Fractional Hermite–Hadamard Inequalities Using m-Convexity and (s, m)-ConvexityAbout the Reduction Method in Fractional Calculus and Fractional Ostrowski Inequalities Readership: Advanced graduate students and researchers interested in time scales, inequalities and difference/differential equations. Key Features:Presents new research on time scales and related inequalitiesMaterials are crucially related to difference/differential equationsSelf-contained chapters that can be read independentlyAn extensive list of references is given in each chapterThe topics covered are diverseKeywords:Time Scale;Fractional Derivative;Difference Equation;Fractional Inequality
Book Synopsis Fractional Differential Equations, Inclusions and Inequalities with Applications by : Sotiris K. Ntouyas
Download or read book Fractional Differential Equations, Inclusions and Inequalities with Applications written by Sotiris K. Ntouyas and published by MDPI. This book was released on 2020-11-09 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Intelligent Comparisons: Analytic Inequalities by : George A. Anastassiou
Download or read book Intelligent Comparisons: Analytic Inequalities written by George A. Anastassiou and published by Springer. This book was released on 2015-07-11 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents recent and original work of the author on inequalities in real, functional and fractional analysis. The chapters are self-contained and can be read independently, they include an extensive list of references per chapter. The book’s results are expected to find applications in many areas of applied and pure mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, as well as Science and Engineering University libraries.
Book Synopsis Applications Of Fractional Calculus In Physics by : Rudolf Hilfer
Download or read book Applications Of Fractional Calculus In Physics written by Rudolf Hilfer and published by World Scientific. This book was released on 2000-03-02 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and collects easily accessible review articles surveying those areas of physics in which applications of fractional calculus have recently become prominent.
Book Synopsis Fractional Differential Equations by : Igor Podlubny
Download or read book Fractional Differential Equations written by Igor Podlubny and published by Elsevier. This book was released on 1998-10-27 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'. This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models. In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research. A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications. A unique survey of many applications of fractional calculus Presents basic theory Includes a unified presentation of selected classical results, which are important for applications Provides many examples Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives
Book Synopsis Fractional Order Analysis by : Hemen Dutta
Download or read book Fractional Order Analysis written by Hemen Dutta and published by John Wiley & Sons. This book was released on 2020-08-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy. Comprehensive in scope, the book covers a range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculus Offers a balance of theory, methods, and applications Puts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological models Helps make research more relevant to real-life applications Written for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.
Book Synopsis The Analysis of Fractional Differential Equations by : Kai Diethelm
Download or read book The Analysis of Fractional Differential Equations written by Kai Diethelm and published by Springer. This book was released on 2010-08-18 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.
