analysis of an age structured sir epidemic model with fractional caputo derivative

In this paper, we consider a mathematical model with fractional derivatives in the sense of caputo with respect to time. it describes the spread of an infectious disease that is directly transmitted in an age-structured population and whose transmission coefficient varies with age. we formulate the basic model as an abstract fractional cauchy problem on a banach space to prove the existence, and uniqueness of a local mild solution and ensure the global existence of a solution. moreover, the results for the existence and uniqueness of non-trivial steady states are also demonstrated under the appropriate conditions.