An Estimate of the Bound of the Lyapunov Exponents for Caputo–Hadamard Fractional Differential System

Abstract

This paper is devoted to estimating the bound of the Lyapunov exponents for the Caputo–Hadamard fractional differential system. First, using the Gronwall inequality, we analyze the continuous dependence of the solution to the Caputo–Hadamard fractional initial value problem (IVP). Then, we define the Lyapunov exponents for the Caputo–Hadamard fractional differential system and estimate their bounds. Besides, numerical examples are displayed which support the theoretical results.