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Question: intsolve error for Abel integral equation

Question:intsolve error for Abel integral equation

danielpf 25 Maple
abel intsolve
February 13 2022
1

The Abel integral equation of the form

g(x) =  Int( f(y) / (x-y)^alpha, y = 0 .. x ) assuming alpha>0, alpha<1;

is linear and has a well known explicit solution for f(x).  

It is a particular form of Volterra equation of the first kind. 

It occurs in many problems of physics with alpha = 1/2.

However intsolve gives an error message:

> eq := g(x) =  Int(f(y)/(x-y)^alpha, y = 0 .. x) assuming alpha>0, alpha<1

> intsolve(eq, f(x));
Error, (in intsolve) numeric exception: division by zero

Replacing (x-y)^alpha by sqrt(x-y) gives the same error message.
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