RC-FODS algorithm for solving numerical solutions of fractional order dynamical system

Abstract

We present a new method, the solving fractional order dynamical systems using reservoir computing (RC-FODS) algorithm, for solving fractional order nonlinear dynamical systems using deep learning. The method is shown to have advantages over traditional methods, such as less calculation time and higher accuracy. This study also compares the RC-FODS algorithm with the traditional recurrent neural network and echo state network algorithms and finds that it has a higher accuracy and shorter computation time. The accuracy of the method is validated using the largest Lyapunov exponent, and the study also analyzes the advantages and disadvantages of different deep learning models. Our study concludes that the RC-FODS algorithm is a promising method for solving fractional order nonlinear dynamical systems with a high accuracy and low error rate.