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Friday, April 24, 2020 | History

3 edition of Generalized functions for the fractional calculus found in the catalog.

Generalized functions for the fractional calculus

Generalized functions for the fractional calculus

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  • 17 Currently reading

Published by National Aeronautics and Space Administration, Glenn Research Center, National Technical Information Service, distributor in [Cleveland, Ohio], [Springfield, Va .
Written in English

    Subjects:
  • Calculus.,
  • Laplace transformation.

  • Edition Notes

    StatementCarl F. Lorenzo, Tom T. Hartley.
    SeriesNASA/TP -- 1999-209424., NASA technical paper -- 209424.
    ContributionsHartley, T. T. 1964-, NASA Glenn Research Center.
    The Physical Object
    FormatMicroform
    Pagination1 v.
    ID Numbers
    Open LibraryOL15560417M


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Generalized functions for the fractional calculus Download PDF EPUB FB2

Recent Application of Fractional Calculus to Science and Engineering (PDF 31P) This note covers the following topics: The Weyl fractional integral and the Mellin transform, Electrical circuits with fractance, Generalized voltage divider, Fractional calculus in viscoelasticity, Fractional order multipoles in electromagnetism.

Generalized Fractional Calculus and Applications Hardcover – Decem 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.

Cited by: This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the : National Aeronautics and Space Administration NASA.

Fractional Calculus is the branch of calculus that generalizes the derivative of a function to non-integer order, allowing calculations such as deriving a function to 1/2 order.

Despite “generalized” would be a better option, the name “fractional” is used for denoting this kind of Size: KB. Generalized Functions for the Fractional Generalized functions for the fractional calculus book Carl F. Lorenzo National Aeronautics and Space Administration Glenn Research Center Cleveland, Ohio Tom T.

Hartley The University of Akron Department of Electrical Engineering Akron, Ohio – Introduction Previous papers have used two important functions for the solution of. For more detailed study Generalized functions for the fractional calculus book generalized functions for fractional calculus and generalized special functions in applied sciences, see e.g.

the classical books (Diethelm ;Erdélyi et al. Fractional calculus and integral transforms of generalized functions. San Francisco ; London: Pitman, (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: A C McBride.

Generalized fractional integrals and derivatives involving Fox's H-function. Special cases, decomposition and applications of the generalized fractional differintegrals in solving Abel type integral equations.

Solutions to dual integral equations with H- and G-functions via the generalized fractional integrals. [Show full abstract] fractional calculus, respectively—as generalized fractional “derivatives” and “integrals.” A solution of the homogeneous ODE of this kind, Dy(z)=λy(z),λ≠0,0Author: Virginia Kiryakova.

Fractional calculus is a generalization of ordinary differentiation and integration to arbitrary (non-integer) order. Generalized functions for the fractional calculus book The subject is as old as the differential calculus, and goes back to times when Leibnitz and Generalized functions for the fractional calculus book invented differential calculus.

The most common notations for β-th. This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R -function and the G -function, useful in analysis and as a basis for computation in the fractional calculus.

The R -function is unique in that it contains all of the derivatives and integrals of the F-function.

Commences with the historical development Generalized functions for the fractional calculus book fractional calculus, its mathematical theory—particularly the Riemann-Liouville version.

Numerous examples and theoretical applications of the theory are presented. Features topics associated with fractional differential equations. Discusses Weyl fractional calculus and some of its uses. FRACTIONAL CALCULUS OF THE GENERALIZED WRIGHT FUNCTION Anatoly A. Kilbas 1 Dedicated to Acad. Bogoljub Stankovic, on the occasion of his th birthday Abstract The paper is devoted to the study of the fractional calculus of the gen-eralized Wright function p“q(z) deflned for z 2 C, complex ai;bj 2 C andFile Size: KB.

COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle.

Abstract. A survey is given on some numerical Generalized functions for the fractional calculus book of Riemann-Liouville fractional calculus. The topics discussed here will be: (a) approximation of fractional derivatives by generalized finite differences and their use in numerical treatment of fractional differential equations, (b) discretized fractional calculus and its use in numerical treatment of Abel type integral equations of first.

Generalized fractional calculus and applications (no Introduction) convolutions, new representations of hypergeometric functions, solutions to classes of differential and integral equations, transmutation method, and generalized integral transforms.

and generalized integral transforms. Some open problems are also book is. For some elementary functions, explicit formula of fractional drevative and integral are presented. Also we present some applica-tions of fractional calculus in science and engineering.

2 Different Definitions In this section we consider different definitions of fractional calculus. Euler(): Euler generalized the formula dnxm dxnFile Size: KB. ­The Fractional Trigonometry: With Applications to Fractional Differential Equations and Science is the result of the authors’ work in fractional calculus, and more particularly, in functions for the solutions of fractional di­fferential equations, which is fostered in the behavior of generalized exponential functions.

The authors discuss. Fractional calculus is a generalization of ordinary calculus which introduces derivatives and integrals of fractional order. Recently, several authors have shown that fractional calculus is a powerful modeling tool to represent the behavior of a number of mechanical, chemical and electrical dynamic systems (Magin, ; San Jose Martinez et al., ; Catania and.

in my opinion, this book fits the category you are asking The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order The product of a collaboration between a mathematician and a chemist, this text is gea. Part 1 of this book presents an introduction to fractional calculus.

Chapter 1 briefly gives definitions and notions that are needed later in the book and Chapter 2 presents definitions and some of the properties of fractional integrals and derivatives. Part 2 is the central part of the book. What enables super calculus in this text is just this property of the generalized binomial coefficient.

Newton is great. 04 Higher Integral (1) Definitions and Notations The 1st order primitive function of f(x) is usually denoted F(x). However, such a notation is unsuitable for the description of the 2nd or more order primitive functions.

Then, fFile Size: KB. The Applications of Generalized Functions by Author Unknown and a great selection of related books, art and collectibles available now at In the fractional calculus approach, the memory functions, which are kernels of the integro-differential operators, are considered to be of the power-law type [41,42,43].

In this paper, we propose an approach that allows us to describe a wide class of memory functions by using the methods of fractional calculus. Now, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations.

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and.

Erdélyi A. () Fractional integrals of generalized functions. In: Ross B. (eds) Fractional Calculus and Its Applications. Lecture Notes in Mathematics, vol Cited by: This paper builds upon our recent paper on generalized fractional variational calculus (FVC).

Here, we briefly review some of the fractional derivatives (FDs) that we considered in the past to develop FVC. We first introduce new one parameter generalized fractional derivatives (GFDs) which depend on two functions, and show that many of the one-parameter FDs considered in Cited by: 5.

A Collection of Fractional Calculus Books (Last updated: 4/8/) (Download the DOCX file. Please send an email to suggest a missing entry. Thank you!) N. Su: Fractional Calculus in Soil Hydrology and Mechanics: Fundamentals and Applications. CRC Press,pages, ISBN Amazon. This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods.

The fractional calculus (FC) may be considered an old and yet novel topic. It is an old topic because, starting from some speculations of G.W. Leibniz (, ) and L. Euler (), it has been developed progressively up to now. However, it may be considered a novel topic as well.

Only since the Seventies, the FC has been the object of specialized conferences and by: The advantages of fractional calculus have been described and pointed out in the last few decades by many authors.

Fractional calculus is based on derivatives and integrals of non integer arbitrary order, fractional differential equations and methods of their solution, approximations and implementation techniques. It hasFile Size: 6MB. The fact is, the book provides a solid basis for so much more, including engineering applications (as illustrated on pp.and these are in /5(15).

April 9, World Scienti c Book - 9in x 6in MAINARDI_BOOK-FINAL Ch. 1: Essentials of Fractional Calculus 5 The fractional derivative with support in IR+ After the notion of fractional integral, that of fractional derivative of order (>0) becomes a natural requirement and one is attempted to substitute with in the above formulas.

book devoted to fractional calculus in Nowadays, to our knowledge, the list of texts in book form with a title explicitly devoted to fractional calculus (and its applications) includes around ten titles, use of generalized functions related to the Dirac "delta function" in the typical way suitable for applications in physics and.

Generalized Functions for the Fractional Calculus and Dirichlet Averages 1 Farooq Ahmad, 2 D. Jain and 3 Renu Jain 1 School of Mathematics and Allied Sciences Jiwaji University, Gwalior (M.P), India 2 Department of Applied Mathematics Madhav Institute of Technology and Science Gwalior (M.P), IndiaAuthor: Farooq Ahmad, D.

Jain, Renu Jain. ­The Fractional Trigonometry: With Applications to Fractional Differential Equations and Science is the result of the authors’ work in fractional calculus, and more particularly, in functions for the solutions of fractional di­fferential equations, which is fostered in the behavior of generalized exponential functions.

The authors discuss. These author’s studies have lead to the introduction and development of a theory of generalized fractional calculus (GFC) in her monograph () and subsequent papers, and to various applications of this GFC in other topics of analysis, differential equations, special functions and integral by: WORKSHOP ON FRACTIONAL CALCULUSSKOPJE R.

MACEDONIA 1 GENERALIZED FRACTIONAL CALCULUS OPERATORS OF RIEMANN-LIOUVILLE AND CAPUTO TYPE AND CAUCHY PROBLEMS Virginia KIRYAKOVA Institute of Math. & Inform. - Bulgarian Academy of Sciences Both in classical and in Fractional Calculus (FC), the notions of derivatives.

fundamental criteria for a generalized calculus established by Ross () are shown to hold for the generalized fractional calculus under appropriate conditions.

A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure. Fractional Calculus: Integral and Pdf Equations of Fractional Order We now observe that an alternative definition of fractional derivative, orig-inally introduced by Caputo [19], [27] in the late sixties and adopted by Ca-puto and Mainardi [28] in File Size: KB.Fractional Differential Equations: An Download pdf to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications - Ebook written by Igor Podlubny.

Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Fractional Author: Igor Podlubny.A Unified Theory of Ebook Differentiation and Ebook (Third Edition): A NEW APPROACH TO FRACTIONAL CALCULUS - The subject of this book is the fractional calculus which treats differentiation and integration to fractional order.

This book presents a new approach to the fractional calculus being based on linear differentiator-like operators to arbitrary order.