Fractional Integrals And Potentials
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Fractional Integrals and Potentials
Author | : Boris Rubin |
Publsiher | : CRC Press |
Total Pages | : 428 |
Release | : 1996-06-24 |
Genre | : Mathematics |
ISBN | : 0582253411 |
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This volume presents recent developments in the fractional calculus of functions of one and several real variables, and shows the relation of this field to a variety of areas in pure and applied mathematics. Beyond some basic properties of fractional integrals in one and many dimensions, it contains a mathematical theory of certain important weakly singular integral equations of the first kind arising in mechanics, diffraction theory and other areas of mathematical physics. The author focuses on explicit inversion formulae that can be obtained by making use of the classical MarchaudĂs approach and its generalization, leading to wavelet type representations.
Fractional Integrals Potentials and Radon Transforms
Author | : Boris Rubin |
Publsiher | : Unknown |
Total Pages | : 0 |
Release | : 2024-05 |
Genre | : Mathematics |
ISBN | : 1032674997 |
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"Fractional Integrals, Potentials, and Radon Transforms, Second Edition presents recent developments in the fractional calculus of functions of one and several real variables, and shows the relation of this field to a variety of areas in pure and applied mathematics. In this thoroughly revised new edition, the book aims to explore how fractional integrals occur in the study of diverse Radon type transforms in integral geometry. Beyond some basic properties of fractional integrals in one and many dimensions, this book also contains a mathematical theory of certain important weakly singular integral equations of the first kind arising in mechanics, diffraction theory and other areas of mathematical physics. The author focuses on explicit inversion formulae that can be obtained by making use of the classical Marchaud's approach and its generalization, leading to wavelet type representations. This book is suitable for mathematical physicists and pure mathematicians researching in the area of integral equations, integral transforms, and related harmonic analysis"--
Fractional Integrals Potentials and Radon Transforms
Author | : Boris Rubin |
Publsiher | : CRC Press |
Total Pages | : 1501 |
Release | : 2024-08-14 |
Genre | : Mathematics |
ISBN | : 9781040101940 |
Download Fractional Integrals Potentials and Radon Transforms Book in PDF, Epub and Kindle
Fractional Integrals, Potentials, and Radon Transforms, Second Edition presents recent developments in the fractional calculus of functions of one and several real variables, and shows the relation of this field to a variety of areas in pure and applied mathematics. In this thoroughly revised new edition, the book aims to explore how fractional integrals occur in the study of diverse Radon type transforms in integral geometry. Beyond some basic properties of fractional integrals in one and many dimensions, this book also contains a mathematical theory of certain important weakly singular integral equations of the first kind arising in mechanics, diffraction theory and other areas of mathematical physics. The author focuses on explicit inversion formulae that can be obtained by making use of the classical Marchaud’s approach and its generalization, leading to wavelet type representations. New to this Edition Two new chapters and a new appendix, related to Radon transforms and harmonic analysis of linear operators commuting with rotations and dilations have been added. Contains new exercises and bibliographical notes along with a thoroughly expanded list of references. This book is suitable for mathematical physicists and pure mathematicians researching in the area of integral equations, integral transforms, and related harmonic analysis.
Introduction to Radon Transforms
Author | : Boris Rubin |
Publsiher | : Cambridge University Press |
Total Pages | : 595 |
Release | : 2015-11-12 |
Genre | : Mathematics |
ISBN | : 9780521854597 |
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A comprehensive introduction to basic operators of integral geometry and the relevant harmonic analysis for students and researchers.
Generalized Fractional Calculus and Applications
Author | : Virginia S Kiryakova |
Publsiher | : CRC Press |
Total Pages | : 412 |
Release | : 1993-12-27 |
Genre | : Mathematics |
ISBN | : 0582219779 |
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In this volume various applications are discussed, in particular to the hyper-Bessel differential operators and equations, Dzrbashjan-Gelfond-Leontiev operators and Borel type transforms, convolutions, new representations of hypergeometric functions, solutions to classes of differential and integral equations, transmutation method, and generalized integral transforms. Some open problems are also posed. This book is intended for graduate and post-graduate students, lecturers, researchers and others working in applied mathematical analysis, mathematical physics and related disciplines.
Hypersingular Integrals and Their Applications
Author | : Stefan Samko |
Publsiher | : CRC Press |
Total Pages | : 382 |
Release | : 2001-10-25 |
Genre | : Mathematics |
ISBN | : 0415272688 |
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Hypersingular integrals arise as constructions inverse to potential-type operators and are realized by the methods of regularization and finite differences. This volume develops these approaches in a comprehensive treatment of hypersingular integrals and their applications. The author is a renowned expert on the topic. He explains the basics before building more sophisticated ideas, and his discussions include a description of hypersingular integrals as they relate to functional spaces. Hypersingular Integrals and Their Applications also presents recent results and applications that will prove valuable to graduate students and researchers working in mathematical analysis.
Fractional Integrals and Derivatives
Author | : Yuri Luchko |
Publsiher | : Mdpi AG |
Total Pages | : 0 |
Release | : 2021-02-16 |
Genre | : Computers |
ISBN | : 3036504958 |
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This Special Issue is devoted to some serious problems that the Fractional Calculus (FC) is currently confronted with and aims at providing some answers to the questions like "What are the fractional integrals and derivatives?", "What are their decisive mathematical properties?", "What fractional operators make sense in applications and why?'', etc. In particular, the "new fractional derivatives and integrals" and the models with these fractional order operators are critically addressed. The Special Issue contains both the surveys and the research contributions. A part of the articles deals with foundations of FC that are considered from the viewpoints of the pure and applied mathematics, and the system theory. Another part of the Special issue addresses the applications of the FC operators and the fractional differential equations. Several articles devoted to the numerical treatment of the FC operators and the fractional differential equations complete the Special Issue.
Theory and Numerical Approximations of Fractional Integrals and Derivatives
Author | : Changpin Li (Mathematics professor),Min Cai (Mathematician) |
Publsiher | : Unknown |
Total Pages | : 312 |
Release | : 2019 |
Genre | : Fractional calculus |
ISBN | : 1611975875 |
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"This book provides a comprehensive review of fractional calculus, covering both theory and numerical methods, and presents recent results on the subject"--