Reddit reviews The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order (Dover Books on Mathematics)
We found 4 Reddit comments about The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order (Dover Books on Mathematics). Here are the top ones, ranked by their Reddit score.
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