<abstract><p>The traditional compartmental epidemic models such as SIR, SIRS, SEIR consider mortality rate as a parameter to evaluate the population changes in susceptible, infected, recovered, and exposed. We present a modern model where population changes in mortality are also considered as the parameter. The existing models in epidemiology always construct a system of the closed medium in which they assume that new birth, as well as new death, will not be possible. But in real life, such a concept will not be assumed to not exist. From our wide observation, we find that the changing rate in every population case is notably negligible, That's why we are preferring to calculate them fractionally using FFDE. Using Lofti's fuzzy concept we are picturing the models after that we are estimating their non-integer values using three distinct methodologies LADM-4, DTM-4 for arbitrary fractional-order $ \alpha_i $, and RKM-4. At $ \alpha_{i} = 1, $ comparison of the estimations will be done. In addition to the simulation, works of numerical estimations, the existence of steady states, equilibrium points, and stability analysis are all done.</p></abstract>