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

by Keith B. Oldham, Jerome Spanier

The product of a collaboration between a mathematician and a chemist, this text is geared toward advanced undergraduates and graduate students. Not only does it 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. Rather than an exhaustive treatment, it represents an introduction that will appeal to a broad spectrum of students. Accordingly, the mathematics is kept as simple as possible.
The first of the two-part treatment deals principally with the general properties of differintegral operators. The second half is mainly oriented toward the applications of these properties to mathematical and other problems. Topics include integer order, simple and complex functions, semiderivatives and semi-integrals, and transcendental functions. The text concludes with overviews of applications in the classical calculus and diffusion problems.

Genres: Mathematics, Reference

234 pages, Paperback

First published June 1, 1974

Reviews

[Jafet]

Es un libro que se me complico bastante ya que está construido con el enfoque de usar series hipergeométricas, pero tiene temas interesantes debido a que la mitad del libro son ejemplos de aplicación de la teoría fraccionaria a química y física. En particular me gusto como a partir de la integral de Cauchy define la integral fraccionaria sin recurrir al clásico método de integración repetida ni depender del teorema de Fubini de intercambio del orden de integrales

[Michael]

Lots of neat formulas about hypergeometric functions, but it felt disjointed - like it was a series of papers stapled together.

If you read it, I recommend reading the chapters in the order: 1, 2, 3, 5, 9, 4, 6, 7, 10, 8, 11.