  In this paper, based on analytic technique, several properties of holographic
$ s $-wave superconductors have been investigated in the presence of various
higher derivative (\textit{non linear}) corrections to the usual Maxwell
action. Explicit expressions for the critical temperature and the condensation
values have been obtained in the probe limit. Finally, the nature of condensate
solutions have been investigated by immersing the superconductor in an external
magnetic field. It is found that below certain critical magnetic field strength
($ B_c $) there exists a superconducting phase. Most importantly it has been
observed that the value of this critical field strength ($ B_c $) indeed gets
affected due to the presence of higher derivative corrections to the usual
Maxwell action.
