2 edition of **Fractional integrals and potentials** found in the catalog.

Fractional integrals and potentials

Boris Rubin

- 20 Want to read
- 7 Currently reading

Published
**1996**
by Longman in Harlow
.

Written in English

- Fractional calculus.,
- Functions.

**Edition Notes**

Bibliography: 397-409.

Statement | Boris Rubin. |

Series | Pitman monographs and surveys in pure and applied mathematics -- 82 |

Classifications | |
---|---|

LC Classifications | QA314 .R82 1996 |

The Physical Object | |

Pagination | xiv, 409 p. ; |

Number of Pages | 409 |

ID Numbers | |

Open Library | OL19837606M |

ISBN 10 | 0582253411 |

Next we are going to discuss the fractional integrals on the Heisenberg group. For given \(\alpha \in (0,Q)\) with \(Q=2n+2\), the fractional integral operator \(I_{\alpha }\) (also referred to as the Riesz potential) is defined by (see). The known proof is very lengthy and complicated and by this reason it was never included into known books of fractional integrals. We suggest a new proof which is easy and brief and also allows to.

This book contains a brief historical introduction and state of the art in fractional calculus. The author introduces some of the so-called special functions, in particular, those which will be directly involved in calculations. The concepts of fractional integral and fractional derivative are also presented. Fractional Calculus, pp. () No Access Fractional Calculus in Multidimensional Space — 3D-Folded Potentials in Cluster Physics - a Comparison of Yukawa and Coulomb Potentials with Riesz Fractional Integrals.

6 Integral transforms compositions method for transmutations 9 Fractional powers of Bessel operators 10 B-potentials theory 11 Fractional differential equations with singular coefficients Conclusion References. A big part of the book is devoted to the fractional calculus. This volume is well structured and has useful content. the books on fractional diﬀerential equation by Podlubny [7] and an introduction to fractional The fractional integrals and potentials are described in the monograph by Rubin [12], the univalent functions, fractional calculus and their applications are described in .

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Fractional Integrals and Potentials (Monographs and Surveys in Pure and Applied Mathematics) 1st Edition by Boris Rubin (Author)Cited by: 1st Edition Published on J by Chapman and Hall/CRC This volume presents recent developments in the fractional calculus of functions of one and sever Fractional Integrals and Potentials - 1st Edition - Boris Rubin - G F.

Buy Fractional Integrals and Potentials by Boris Rubin online at Alibris. We have new and used copies available, in 1 editions - starting at $ Shop Range: $ - $ Preface Notation Chapter 1 Generalities Chapter 2 One-dimensional fractional integrals Chapter 3 Fractional integro-differentiation via wavelet transforms Chapter 4 Riesz potentials on R Chapter 5 Oscillatory potentials on R Chapter 6 Potentials on a half-space Chapter 7 Riesz potentials on a ball Chapter 8 Fractional integrals on a sphere.

Fractional Integrals and Derivatives: Theory and Applications Stefan G. Samko, Anatoly A. Kilbas, Oleg I. Marichev This monograph is devoted to the systematic and comprehensive exposition of classical and modern results in the theory of fractional integrals and their applications.

This chapter reviews some basic properties of fractional integrals and derivatives. Asymptotic behavior of the left Riemann–Liouville fractional integral is then characterized, followed by a discussion of Riesz potentials and Riesz derivatives.

Next, the chapter defines the symmetrized Caputo fractional derivative of an absolutely continuous function. B. Rubin: Fractional integrals and potentials. Chapman and Hall/CRC,pages, ISBN (Google books) T.

Runst, W. Sickel: Sobolev spaces of fractional order, Nemytskij operators, and nonlinear partial differential equations. Walter de Gruyter,pages, ISBN: (Google books) Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors.

The methods of integral transforms via local fractional calculus have been used to solve. for fractional integral operators, also known as Riesz potentials, and for commutators of fractional integrals.

Our point of view is strongly in uenced by the groundbreaking work on dyadic operators that led to the proof of the A 2 conjecture by Hyt onen [43] and the simpli cation of that proof by Lerner [58,59].

(See also [42] for a more. Riemann-Liouville Fractional Integrals and Derivatives 28 The Abel integral equation 29 On the solvability of the Abel equation in the space of integrable functions 30 Definition of fractional integrals and derivatives and their simplest properties 33 Fractional integrals and derivatives of complex order 38 Abstract.

This chapter introduces an important class of transmutations, namely, Buschman–Erdélyi integral and transmutation operators. For example Riemann–Liouville fractional integrals, classical Sonine and Poisson operators, and Mehler–Fock transforms are special cases of this class.

In this chapter our aim is to introduce grand Morrey spaces in the framework of quasimetric measure spaces with doubling measures and study the boundedness of maximal, fractional, and singular integral operators.

We explore also mapping properties of commutators of Calderón–Zygmund singular integrals and potentials with BMO functions. Bibliography Includes bibliographical references (p. []) and indexes. Contents. Fractional integrals and derivatives on an interval-- fractional integrals and derivatives on the real axis and half-axis-- further properties of fractional integrals and derivatives-- other forms of fractional integrals and derivatives-- fractional integrodifferentiation of functions of many variables.

The tautochrone under arbitrary potentials using fractional derivatives. but the details can be found in Oldham and Spanier’s book. 2, pages the integral are given, and their. Fractional Integrals and Potentials by Boris Rubin (Hardback, ) Be the first to write a review.

The lowest-priced brand-new, unused, unopened, undamaged item. Boris Rubin is Professor of Mathematics at Louisiana State University.

He is the author of the book Fractional Integrals and Potentials and has written more than one hundred research papers in the areas of fractional calculus, integral geometry, and related harmonic analysis. "About this title" may belong to another edition of this title.

New Edition: Fractional Calculus: An Introduction for Physicists (3rd Edition)The book presents a concise introduction to the basic methods and strategies in fractional calculus and enables the reader to catch up with the state of the art in this field as well as to participate and contribute in the development of this exciting research contents are devoted to the application of.

The approach, suggested by N. Engheta, is based on the fractional-order differentiation of the Dirac delta function (see formula ()), and allows formulation of electric source distributions whose potentials are obtained by fractional differentiation or integration of potentials of.

Fractional Derivatives, Fractional Integrals, and Fractional Differential Equations in Matlab Ivo Petrá Technical University of Ko ice Slovak Republic uction The term fractional calculus is more than years old. It is a generalization of the ordinar y differentiation and integration to. Fractional Integrals on the Half-Line 39 Decreasing Fractional Integrals and Wavelet Measures 45 Fractional Derivatives on the Half-Line 52 Regularization of Integrals with Power Singularity and Analytic Continuation of Fractional Integrals 61 Some Other Fractional Integrals 64 Notes to Chapter 2 81 3 Riesz Potentials.

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.The Fractional Calculus; Theory and Applications of Differentiation and Integration to Arbitrary Order.

Mathematics in Science and Engineering. V. Academic Press. ISBN Miller, Kenneth S.; Ross, Bertram, eds. (). An Introduction to the Fractional Calculus and Fractional Differential Equations.

John Wiley & Sons.The well known Balakrishnan formula represents the fractional power (–A) α in case of the generator A of a semigroup T t, t > 0, in terms of a (hyper)-singular integral with .