Chaos Detection in Generalized ψ-Fractional Differential Systems

Abstract

This article focuses on investigating fractional Lyapunov exponents for generalized ψ-fractional differential systems. By employing a new and more suitable definition, we derive an expression for the fractional Lyapunov exponents using the inverse of the Mittag-Leffler function, which depends on the kernel, weight, and order of the considered fractional derivative. We also provide an upper bound for the obtained fractional Lyapunov exponents that is tighter than the one available in existing literature. Finally, experiments conducted on a hyperchaotic 5D system and the well-known Lorenz system serve to illustrate and verify our main results.