The paper suggests algorithms for identifying parameters of exponential trend models in the presence of fractional white noise. The paper considers three types of models that are solutions of a homogeneous linear differential equation of the second order. Identification of the solution of a differential equation makes it possible to increase accuracy by taking into account a priori information about the nature of the roots of the differential equation and initial conditions. However, identification of the solution is fraught with difficulties due to nonlinearity in the parameters of the obtained solutions. Two-step algorithms are proposed, allowing to determine the estimates of the parameters of the considered trend models. Test examples showed high accuracy of the estimates obtained using the developed algorithms.