I am looking for a reference that provides a detailed solution for weakly singular integrals of type: $$(T_\gamma \phi)(x)=\int_0^1|x-y|^{-\gamma}\phi(y)dy=f(x)$$ where $f(x)$ is known and $\phi$ is the unknown function to be found. In particular, I would like to get references where numerical approximations for the index $\gamma$ is found for $0<\gamma<1$. I checked the references below but I was unable to find an example of the type above.
References
Muskhelishvili, N. I. (2008). Singular Integral Equations: Boundary Problems of Function Theory and Their Application to Mathematical Physics (Dover Books on Mathematics).
Erdogan, F. (1969). Approximate solutions of systems of singular integral equations. SIAM Journal on Applied Mathematics, 17(6), 1041-1059.
I found the following book which contains most of what I was looking for:
Delves, L. M., & Mohamed, J. L. (1988). Computational methods for integral equations. Cambridge University Press
Any similar reference(s) is welcome.