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Theory and applications of fractional differential equations - Google Books Result - NSF REU Site on Applied Fractional Calculus (AFC) (a proposal) (AFC labs) (AFC REU sample projects). Project: e-Collection of Bruce J. West's papers (DVD: ...
Generalized fractional calculus and applications - Google Books Result - New Trends in Nanotechnology and Fractional Calculus Applications - In recent years fractional calculus has played an important role in various fields such ...
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The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order (Dover Books on Mathematics)
Feature: ... ISBN13: 9780486450018; Condition: New; Notes: BUY WITH CONFIDENCE, Over one million books sold! 98% Positive feedback. Compare our books, prices and service to the competition. 100% Satisfaction Guaranteed ...more
Customer Reviews — [1] Rating: 4 Date: 2007-02-03 Summary: A classical book ... The Fractional Calculus by Keith B. Oldham is a classic book on the topic. To my best knowledge, it was the first book devoted exclusively on fractional calcylus. It includes a useful tables of fractional derivatives. It also discuss in detail many of the original dmathematical derivations that in more recent books are simply ommited by citing the Oldham's book. Unfortunately, in some parts its notation is a little complicated and not intuitive. Any way, it is a mandatory reference in any worl on fractional calculus. ...more
[2] Rating: 5 Date: 2006-07-19 Summary: Excellent book! ... This is a great book. The only prerequisite I would say is calc 2 (know your series and integration very well) and perhaps a little bit of ordinary differential equations. ...more
[3] Rating: 5 Date: 1996-12-16 Summary: Summary : An excellent introduction to the field. ... This was the first textbook devoted entirely to Fractional Calculus, and remains perhaps the best introduction to the field. It is a graduate level text for mathematicians, engineers and scientists, written in a clear pedagogical style, with excellent references and bibliography. A brief historical survey traces contributions as far back as Leibnitz. Basic results of the traditional integer-order differential and integral calculus are summarized, and properties of some special functions are examined, as a foundation ...more
Editorial Reviews — ... Product Description | Not only does this text explain the theory underlying the properties of the generalized operator, but it also illustrates the wide variety of fields to which these ideas may be applied. Topics include integer order, simple and complex functions, semiderivatives and semiintegrals, and transcendental functions. 1974 edition. ...more
Stochastic Calculus for Fractional Brownian Motion and Applications (Probability and Its Applications)
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Editorial Reviews — ... Product Description | Fractional Brownian motion (fBm) has been widely used to model a number of phenomena in diverse fields from biology to finance. This huge range of potential applications makes fBm an interesting object of study. fBm represents a natural one-parameter extension of classical Brownian motion therefore it is natural to ask if a stochastic calculus for fBm can be developed. This is not obvious, since fBm is neither a semimartingale (except when H = ½), nor a Markov process so the classical...more
Applications of Fractional Calculus in Physics
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Editorial Reviews — ... Product Description | 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 the mathematics, until recently they have 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...more
Calculus: The Language of Change
Editorial Reviews — ... Product Description | Calculus: The Language of Change is an innovative new introductory textbook that blends reform and traditional approaches with a focus on understanding calculus as its own language. With accessible writing and presentation, the book allows students to gradually understand the language -- first by reviewing vocabulary, and then quickly moving to present calculus conceptually, computationally, and theoretically. Within this framework, derivatives and integrals are developed side-by-side,...more
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Editorial Reviews — ... Product Description | This monograph provides the most recent and up-to-date developments on fractional differential and fractional integro-differential equations involving many different potentially useful operators of fractional calculus. The subject of fractional calculus and its applications (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, due mainly to its demonstrated applications...more
The Fractional Fourier Transform: with Applications in Optics and Signal Processing
Customer Reviews — [1] Rating: 5 Date: 2003-05-22 Summary: I am smarter now ... I am an optical engineering student and felt that this book was quite understandable (although I read the optics back half first, which then motivated the mathematical front half for me). It gave me additional insight into the Fourier transform as well as the applications of Fourier analysis in optics. I also learned as much on optics from this book as I have from any dedicated optics book. It has so many jewels that other books don't have that I wish I was rich enough to own a copy rather than having to check it out ...more
[2] Rating: 5 Date: 2001-04-19 Summary: The aspects of signals and systems in Fractional domains ... From my point of view as a deeply intested reader of the book, this book is an excellent source book for those who want to increase his/her knowledge on concepts of signals and sytems. It is a comprehensive study on the signal and system representation in generalized frequency domains with very useful applications in different era of electrical engineering. Starting with a general representation theory and then focusing on time-frequency representations, the book prepares the reader for the novel generalized Fourier ...more
[3] Rating: 5 Date: 2001-03-16 Summary: Excellent reference on Fractional Fourier Transforms ... This is a delightful reference book on the Fractional Fourier Transform. The authors did a great job explaining systems theory leading up to a thorough treatment of the Fractional Fourier Transform and other fractional transforms. Plenty of references are cited leading the reader to a rich source of background and follow-up material. Later chapters delve into suggested applications which complete a rather pleasing read of the entire subject. Buy this book. ...more
Editorial Reviews — ... Product Description | The discovery of the Fractional Fourier Transform and its role in optics and data management provides an elegant mathematical framework within which to discuss diffraction and other fundamental aspects of optical systems. This book explains how the fractional Fourier transform has allowed the generalization of the Fourier transform and the notion of the frequency transform. It will serve as the standard reference on Fourier transforms for many years to come....more
Fractional Integrals and Derivatives: Theory and Applications
Editorial Reviews — ... Product Description | All existing types of fractional integro-differentiation are examined and compared. The application of fractional calculus to various types of equations is considered. These include first order integral equation (with power, power-logarithmic kernels and special functions in kernels), Euler-Poisson-Darboux-type equations, and differential equations of fractional order. The clear presentation of historical background, the extensive analysis of the great number of cited papers (more than...more
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