Solving Fractional Dynamical System with Freeplay by Combining Memory-Free Approach and Precise Integration Method

Abstract EN

The Yuan-Agrawal (YA) memory-free approach is employed to study fractional dynamical systems with freeplay nonlinearities subjected to a harmonic excitation, by combining it with the precise integration method (PIM).

By the YA method, the original equations are transformed into a set of first-order piecewise-linear ordinary differential equations (ODEs).

These ODEs are further separated as three linear inhomogeneous subsystems, which are solved by PIM together with a predictor-corrector process.

Numerical examples show that the results by the presented method agree well with the solutions obtained by the Runge-Kutta method and a modified fractional predictor-corrector algorithm.

More importantly, the presented method has higher computational efficiency.