On uniform approximations to the solution of the Abel integral equation (Q904392)

The author considers the Abel integral equation in the form \[ \int^x_0\frac{(x-t)^{\beta-1}} {\Gamma(\beta)}u(t)dt=f(x), \] where \(\Gamma\) is the gamma function, \(\beta \in (0,1)\), \(u\in C_{<0,1>}\) and \(f\) is defined by its approximation in \(L_{2}(0,1): \| f_{\delta}-f\|_{L_2}\leq\delta\). She uses the regularization method without restrictions on the parameter.