#1,724 in Science & math books
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Reddit mentions of The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order (Dover Books on Mathematics)
Sentiment score: 1
Reddit mentions: 4
We found 4 Reddit mentions of The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order (Dover Books on Mathematics). Here are the top ones.
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Specs:
Height | 8.50392 Inches |
Length | 5.5118 Inches |
Number of items | 1 |
Release date | April 2006 |
Weight | 0.61949895622 Pounds |
Width | 0.5381879 Inches |
Can't beat Dover books. The reviews are quite good for this one, and the price is right (less than $10).
I'm not very strong in fractional calc, but I've read a little and have a neat little text on it. I might have something that might interest you. The solutions to the Bessel equation is at the bottom and the derivation is what follows.
I don't have the patience to type this out, but basically, for the Bessel equation with the y coefficient being x-v^2 /4, do a substitution of w=x^(pm.5v)u, v= the positve square root of v^(2) and pm=+/-. Then assume u takes a fractional derivative of order .5pmv of some differintegrable function f. Then fractional calculus happens, and then you arrive as the final two solutions of
x^(.5v)d^(.5+v)sin(2sqrt(x))/dx^(.5+v) for nonnegative and noninteger v, and
x^(-.5v)d^(.5-v)sin(2sqrt(x))/dx^(.5-v) for all v>=0
The text is The Fractional Calculus by Oldham and Spanier.
Look on page 80-81 of this book: http://www.amazon.com/dp/0486450015 . It's available in the book preview.
Presumably: The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order