In this paper, we simulate an epidemic model of cholera disease in the sense of generalized Liouville-Caputo fractional derivative. We provide the results related to the existence of a unique solution by using some well-known theorems. Numerical solutions of the given model are derived by using two different numerical methods along with their importance. A number of graphs are plotted to understand the given cholera disease dynamics. The main motivation to do this research is to understand the given disease dynamics as well as the efficiency of both methods which are very recent to the literature.