The authors study the boundness of integral operators \[ Tf(x)=\int_{\mathbb{R}^n}\frac{f(y)}{|x-y|^{n/s}} dy;\qquad S_Mf(x)=\int_{\mathbb{R}^n}\frac{f(y)}{|x-y|^{n/s}(1+|x-y|)^M} dy \] with some \(s>1,M>0\) on generalized Morrey spaces of the type \[ L^\Phi_p= \Biggl\{f\in L^p_{\text{loc}}(\mathbb{R}^n)|\sup_{x\in \mathbb{R}^n, r>0} \frac{1}{\Phi(x,r)}\int_{B(x,r)}|f(y)|^pdy<\infty \Biggr\}, \] where \(\Phi(x,r)>0\) is a weight function with some growth conditions, \(B(x,r)=\{y|\;|x-y|<r\}\) is the ball. The results have applications to norms estimates of the Schrödinger operator \(-\Delta +V(x)+W(x)\) on \(\mathbb{R}^n\) on generalized Morrey spaces with nonnegative \(V\in (RH)_\infty\) (reserve Hölder class: \(\exists C>0\), for each ball \(B=B(x,r)\), \(\sup_{y\in B} |V(y)|\leq \frac{C}{|B|}\int_B|V(y)|dy\)) and small perturbed potentials \(W\).