Parallel Implementation of Modeling of Fractional-Order State-Space Systems Using the Fixed-Step Euler Method

This paper presents new results in implementation of parallel computing in modeling of fractional-order state-space systems. The methods considered in the paper are based on the Euler fixed-step discretization scheme and the Grünwald-Letnikov definition of the fractional-order derivative. Two different parallelization approaches for modeling of fractional-order state-space systems are proposed, which are implemented both in Central Processing Unit (CPU)- and Graphical Processing Unit (GPU)-based hardware environments. Simulation examples show high efficiency of the introduced parallelization schemes. Execution times of the introduced methodology are significantly lower than for the classical, commonly used simulation environment.