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Basic rules of differintegration

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Some basic rules of differintegration when dealing with fractional calculus follow:

Generalized Product Rule

In general, we have the Leibniz rule for n-fold differentiation of a product (see product rule):

for integers n > 0.

For non-integer n, (nj) is defined but nonzero, when j > n, and consequently,

By analogy we expect, instead, for non-integer n,the infinite series

This motivates the product rule of differintegration.

    definition

Book resources

"An Introduction to the Fractional Calculus and Fractional Differential Equations"
by Kenneth S. Miller, Bertram Ross (Editor)
Hardcover: 384 pages ; Dimensions (in inches): 1.00 x 9.75 x 6.50
Publisher: John Wiley & Sons; 1 edition (May 19, 1993)
ASIN: 0471588849

"The Fractional Calculus; Theory and Applications of Differentiation and Integration to Arbitrary Order (Mathematics in Science and Engineering, V)"
by Keith B. Oldham, Jerome Spanier
Hardcover
Publisher: Academic Press; (November 1974)
ASIN: 0125255500

"Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications." (Mathematics in Science and Engineering, vol. 198)
by Igor Podlubny
Hardcover
Publisher: Academic Press; (October 1998)
ISBN: 0125588402