Fractional Order Dynamic Mode Decomposition

This study extends the dynamic mode decomposition (DMD) framework to fractional order DMD, enabling it to handle systems characterized by fractional dynamics. Traditional DMD is based on integer-order differential equations, which can be insufficient for capturing the dynamics of fractional-order systems. In this work, we incorporated fractional order dynamics into the DMD framework. Instead of using exponential functions, the eigen-decomposition of the approximated coefficient matrix was used to determine the parameters of the Mittag-Leffler functions, which were then employed to reconstruct the system's dynamics. Simulation results demonstrate that the fractional order DMD can effectively capture the dynamics of fractional order systems. Additionally, the proposed framework remains applicable to integer order systems as well.