In this paper, we will discuss an analytical solution and numerical simulation of fractional order mathematical model on COVID-19 under Caputo and conformable sense with the help of fractional differential transform method for different values of q, where q ∈ (0, 1). The underlying mathematical model on COVID-19 consists of four compartments, like, the susceptible class, the healthy class,the infected class and the quarantine class. We show the reliability and simplicity of the methods by comparing the solution of given model obtained by FDTM with the solution obtained by CFDTM graphically and numerically. Further, we analyse the stability of model using Lyapunov direct method under Caputo sense. We conclude that the use of fractional epidemic model provides better understanding and biologically deeper insights about the disease dynamics.