Re: Fractional Integral Equation

From: Alain Verghote (alainverghote_at_yahoo.fr)
Date: 08/25/04 

Date: Wed, 25 Aug 2004 21:30:02 +0000 (UTC)

On Wed, 25 Aug 2004 13:30:01 +0000 (UTC), AL wrote:
>Hello,
>
>
>Does anyone the solution for the following fractional integral
>equation:
>
>A*D^{-b}f(x)+x^{-b}*f(x)=1
>
>In the application b=1/3. Thanks for the help!
>
>
>Greetings, A.L

Dear A.L,

I've read 'your fractional integral equation'.
you want to solve:A*d/dx ^(-1/3) f(x)+ x^(-1/3)*f(x)=1.
A way to consider fractional derivative /integral ,r real is
putting d/dx^[r] (x^k)=Gamma(k+1)/Gamma(k-r+1)*x^(k-r) a
generalization of d/dx^[n] (x^k)=k!/(k-n)!*x^(k-n) n,k integer.
For f(x)=c*x^k we've got:
   A*c*Gamma(k+1)/Gamma(k+4/3)*x^(k+1/3)+c*x^(k-1/3)=1
What means A?.
May be it helps...

Sincerely,Alain.