Application of fractal properties in studies of financial markets

When studying the financial markets, the currency quotations of the Russian ruble / US dollar pair are examined for fractality. It is demonstrated that the time series of the quotations under study has basic fractal properties. Hurst exponent is used here to confirm the hypothesis of fractality whereby Hausdorff dimension was calculated, which turned out to be a fraction. The state of flux graphs were compared with the solution graphs of the known fractional differential equation of a point particle random walk along a self-similar fractal set. The solution of such an equation is given using the Mittag-Leffler functions. The graphs of these solutions are compared with state of flux graphs for different time intervals. Hence, it is proved that the Russian financial market is fractal and these results will help to forecast market behavior for a specified time interval in the future