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We analytically describe the properties of the s-wave holographicsuperconductor with the Exponential nonlinear electrodynamics in the Lifshitzblack hole background in four-dimensions. Employing an assumption the scalarand gauge fields backreact on the background geometry, we calculate thecritical temperature as well as the condensation operator. Based onSturm-Liouville method, we show that the critical temperature decreases withincreasing exponential nonlinear electrodynamics and Lifshitz dynamicalexponent, z, indicating that condensation becomes difficult. Also we find thatthe effects of backreaction has a more important role on the criticaltemperature and condensation operator in small values of Lifshitz dynamicalexponent, while z is around one. In addition, the properties of the uppercritical magnetic field in Lifshitz black hole background using Sturm-Liouvilleapproach is investigated to describe the phase diagram of the correspondingholographic superconductor in the prob limit. We observe that the criticalmagnetic field decreases with increasing Lifshitz dynamical exponent, z, and itgoes to zero at critical temperature, independent of the Lifshitz dynamicalexponent, z.

Exponential nonlinear electrodynamics and backreaction effects on Holographic superconductor in the Lifshitz black hole background