This paper describes the development and approbation of the software solution, which implements the methodology of forming recommendations for the composition of investment portfolios using fractal analysis and long memory predictive models, which is the result of research conducted over several years at the Department of Information Systems and Mathematical Methods in Economics of PSU. The general algorithm of the program includes four main steps: 1) obtaining and preparing data; 2) sorting assets by the fractal dimension of their price series; 3) forecasting asset returns; 4) forming portfolios (determining asset shares). The described algorithm stages correspond to the structure of the program solution, expressed by the set of its subsystems. The features of the developed program are as follows: possibility to load data of share prices from the FINAM website; calculation of the fractal dimension of asset price series by the DFA and minimum coverage methods; asset returns forecasting using the ARFIMA and ARFIMA-GARCH models; selection of portfolio structures based both on the forecasted and historical data; possibility of multiple generation of portfolios based on random-selected assets with characteristics averaging; evaluation of portfolio characteristics using test data (if any); support for multi-core processors for multiple acceleration of calculations; windowed graphical interface. The results of program approbation on the Russian stock market data under crisis economic conditions are given. On the whole, these results are in line with those obtained earlier on the developed US market data. The developed program can be used by portfolio investors, carrying out investment activities in the international financial markets. Scientific application of the program is important: its users can be scientists, students and other researchers of innovative methods of investment portfolios formation.