Modified Comparison Theorems for Solutions of Caputo-Hadamard Fractional Differential Equations

In this paper we primarily focus on modifying comparison theorems with strict and nonstrict inequalities for Caputo-Hadamard fractional differential equations (FDEs). First, we point out that the proof of comparison theorem for Caputo-Hadamard FDEs in the paper (Fractals 2019, 27(3), 1950036) is incorrect. And then, we give a modified comparison theorem for solutions of Caputo-Hadamard FDEs of order p is an element of (0, 1) under strict inequalities, then extend order p to arbitrary positive-order. Finally, we present a modified comparison theorem with nonstrict inequalities for solutions of Caputo-Hadamard FDEs.