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The influence of the fourth-order dispersion coefficient on the behavior of parametric gain and saturation power of a one-pump fiber optical parametric amplifier over a signal wavelength span in the presence of fiber random dispersion fluctuations was investigated. The output signal power for the parametric gain calculation was obtained by numerically solving the three-coupled amplitude equations. Based on the calculations of the parametric gain over a variation of the signal wavelength, it is found that the saturation power behavior is dependent on the behavior of parametric gain. The manipulations of signal wavelength and the fourth-order dispersion coefficient changed the phase-matching condition, thereby affecting the resulting parametric gain and saturation power.