In this paper, we prove approximate solvability of the semilinear operator equations of the form \(Lu+Nu=v\) using fractional Tikhonov regularization and Browder’s fixed point theorem under the following assumptions: (i) The corresponding linear operator equation \(Lu=v\) is approximately solvable where L is a bounded linear operator defined on Hilbert spaces U and V.
(ii) The nonlinear operator \( N: U \rightarrow V\) is compact.
(iii) \(\Vert Nu \Vert \le a+b \Vert u \Vert \) for some positive constants a and b where \(b < \frac{1}{M_{\lambda ,\ \alpha }(M_{\lambda ,\ \alpha }+1)}\) , \(M_{\lambda ,\ \alpha } \) is a constant described in the text.
The theory is substantiated with an application to approximately controllable semilinear control system.
