Fredholm integral equation of the 2nd kind with a weakly singular convolution kernel

Question

I've reviewed the literature but could not find a solution of the integral equation $$\int_{0}^{1} dx\frac{\phi(x)}{|x-y|^{\alpha}}+a\phi(y)=b.$$ for the function $\phi$ where $\alpha\in(0,1)$ and the constants $a,b$ are known.
If anybody knows the solution or has an idea on how to solve this equation, that would be very helpful.
Thanks in advance.