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Analytical expressions of the temporal power spectral models of angle of arrival (AOA) fluctuations are derived using the generalized exponential spectral model for optical waves propagating through weak non-Kolmogorov turbulence. Compared with expressions of temporal power spectral models derived from the general non-Kolmogorov spectral model, the new expressions consider the influences of the inner and outer scales of finite turbulence. Numerical calculations show that large outer scales of turbulence increase the value of the temporal power spectrum of AOA fluctuations in low-frequency regions.