Define the Lyapunov Exponents for ψ-Fractional Differential System

Abstract

In this article, we focus on the relations between the asymptotics of solutions and the sensitivity to initial values of fractional differential systems. To investigate this problem, we consider the ψ-fractional calculus, which is considered to be a generalization of those of Riemann–Liouville and Hadamard. For this purpose, we define Lyapunov exponents for ψ-fractional differential systems and estimate their upper bounds. Examples are presented to demonstrate the accuracy of our results.