In this study, a cascaded dual micro-ring resonator with the same radius is used to implement an n>1 order optical time-domain differentiator. The effects of differentiation accuracy, energy efficiency, and input signal on the differentiation results of the cascaded dual-ring differentiator were analyzed using the principle of minimum average deviation. In comparison with a single micro-ring, the average absolute deviation of differential waveform can be reduced from 5.67% to 0.67%. Within the range of 1<n<2 differential orders, the overall average absolute deviation of the differentiator does not exceed 2.3% and the cross-correlation coefficients are greater than 99%. The differential accuracy is improved, the input signal pulse width is less affected the defferentiation order of the cascaded dual micro-ring defferentiator, and the applicable input-signal pulse width range is larger. Simultaneously, by adjusting the coupling state of a loop in the cascade structure, the differentiation order of the differentiator can be changed to realize a tunable high-precision fractional differentiator.