Fractional Differentiation Inequalities
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Fractional Differentiation Inequalities
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Author : George A. Anastassiou
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-28
Fractional Differentiation Inequalities written by George A. Anastassiou 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 2009-05-28 with Mathematics categories.
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.
Advances On Fractional Inequalities
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Author : George A. Anastassiou
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-25
Advances On Fractional Inequalities written by George A. Anastassiou 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 2011-07-25 with Mathematics categories.
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.
Constructive Fractional Analysis With Applications
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Author : George A. Anastassiou
language : en
Publisher: Springer Nature
Release Date : 2021-04-01
Constructive Fractional Analysis With Applications written by George A. Anastassiou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-01 with Technology & Engineering categories.
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.
Intelligent Analysis Fractional Inequalities And Approximations Expanded
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Author : George A. Anastassiou
language : en
Publisher: Springer Nature
Release Date : 2020-01-15
Intelligent Analysis Fractional Inequalities And Approximations Expanded written by George A. Anastassiou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-15 with Technology & Engineering categories.
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.
Unification Of Fractional Calculi With Applications
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Author : George A. Anastassiou
language : en
Publisher: Springer Nature
Release Date : 2021-11-21
Unification Of Fractional Calculi With Applications written by George A. Anastassiou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-21 with Technology & Engineering categories.
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.
Generalized Fractional Calculus
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Author : George A. Anastassiou
language : en
Publisher: Springer Nature
Release Date : 2020-11-25
Generalized Fractional Calculus written by George A. Anastassiou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-25 with Technology & Engineering categories.
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.
Fractional Hermite Hadamard Inequalities
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Author : JinRong Wang
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-05-22
Fractional Hermite Hadamard Inequalities written by JinRong Wang 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 2018-05-22 with Mathematics categories.
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
Intelligent Comparisons Analytic Inequalities
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Author : George A. Anastassiou
language : en
Publisher: Springer
Release Date : 2015-07-11
Intelligent Comparisons Analytic Inequalities written by George A. Anastassiou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-11 with Technology & Engineering categories.
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.
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. 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
Fractional Differential Equations
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Author : Zhi-Zhong Sun
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-08-24
Fractional Differential Equations written by Zhi-Zhong Sun 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.
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.