The finite Laplace transform for solving a weakly singular integral equation occurring in transfer theory (Q2567982)

The authors consider an integral equation of the type \[ y(x)= 1+ \int^b_0 k(x- t)y(t)\,dt. \] By the finite Laplace transform, the equation is reduced to a singular integral equation over \([-1,1]\) of Cauchy type, which in turn is transformed into a Fredholm integral equation over \([0,1]\).