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(Theory and Application of Differentiation and Integration to Arbitrary Order)

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**About this book :- **
**The Fractional Calculus ** written by
** Keith Oldham, Jerome Spanier**.

The book is divided into two parts. The first six chapter deal principally with the general properties of differintegral operators while chapter 7-11 are mainly oriented toward the application of these properties to mathematical and other problems.

**Book Detail :- **
** Title: ** The Fractional Calculus
** Edition: **
** Author(s): ** Keith B. Oldham, Jerome Spanier
** Publisher: ** Academic Press
** Series: **
** Year: ** 1974
** Pages: ** 240
** Type: ** PDF
** Language: ** English
** ISBN: ** 0125255500
** Country: ** Us
** Get this book from Amazon**

**About Author :- **
** Keith B. Oldham **, Department of Chemistry, Trest University, Peterborough, Ontario and
** Jerome Spanier **, Department of Mathematics, Claremont Graduate School, Claremont, California.
Students of mathematics early encounter the differential operators d/dx, d2/dx2, d3/dx3 etc and some doubtless ponder whether it is necessary for the order differentiation to be an integer. Why should there not be a d1/2/dx1/2 operator, for instance? or d-1/dx-1 etc. I is to these and related equations that the present work is addressed. it will come as no surprise to one versed in the calculus that the operator d-1/dx-1 is nothing but an indefinite integral in disguise but frational orders of differentiation and more mysterious because they have no obvious geometric interpretation along the line of the customary introduction to derivatives and integrals as slopes and areas. The reaer who is prepared to dispense with a pictorial representation, however will soon find that fractional order derivatives and integrals are just as tangible as those of integer order and that a new dimenstion in mathematics opens to him when the order q of the operator d2/dx2 becomes as arbitrary parameter.

**Book Contents :- **
**The Fractional Calculus ** written by
** Keith Oldham, Jerome Spanier**
cover the following topics.

1. Introduction

2. Differentiation and Integration to Integer Order

3. Fractional Derivatives And Integrals, Difinitions And Equivalences

4. Differintegration of Simple Functions5

5. General Properties

6. Differintegration of Moare Complex Functions

7. Semiderivatives and Semiintegrals

8. Techniques in the Fractional Calculus

9. Representation of Transcendental Functions

10. Applications in the Classial Calculus

11. Application to Diffusion Problems

- Abstract Algebra
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