It is known to us that the fractional derivatives are the general case of differentiation, that is to say the normal derivative is a special case of fractional derivative. So, our contribution in this paper based on two paths, the first one aims is to study and estimate the parameters of nonlinear time series models sample with continuous case, known by COGARCH(1,1) with a fractional derivative. Where this study allows testing the generalization estimation algorithm on the fractional COGARCH, second path based to present an estimation comparison between classic COGARCH(1,1) and COGARCH(1, 1) with a fractional derivative. Then, we illustrate our study with simulation to answer some questions and extract some properties.