On the hadamard type fractional differential system

Abstract

The Gronwall inequality, which plays a very important role in clasical differential equations, is generalized to the fractional differential equations with Hadamard derivatives in this paper. According to the inequality, we investigate the dependence of the solution on both the order and the initial conditions to the fractional differential equations with Hadamard derivatives. Furthermore, in terms of the inequality, the estimation of the bound of the Lyapunov exponents for the Hadamard type fractional differential systems is considered.