COMPARISON THEOREMS FOR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS

The main purpose of this paper is to investigate the comparison theorems for fractional differential equations involving Caputo-Hadamard fractional derivatives. First, we indicate the continuous dependence on parameters of solutions for Caputo-Hadamard fractional differential equations (C-HFDEs). Then, the first and second comparison theorems for C-HFDEs are proposed and proved, respectively. In addition, we establish the generalized comparisons for C-HFDEs under the one-side Lipschitz conditions. At last, the corresponding examples are also provided to verify the theoretical results.