In this paper we propose two problems which related to fractional Brownian motion. First problem- simultaneous estimation of two parameters-Hurst exponent and the volatility, that describes this random process. Numerical tests for the simulated fBm provided an efficient method. Second problem- approximation of the increments of observed time series with power function by increments from the fractional Brownian motion. Approximation and estimation have shown on the example of real data- daily deposit interest rates.