Necessary optimality conditions of a reaction-diffusion SIR model with ABC fractional derivatives

<p style='text-indent:20px;'>The main aim of the present work is to study and analyze a reaction-diffusion fractional version SIR epidemic mathematical model by means non-local non-singular ABC derivative operator with complete memory effects. Existence uniqueness solution for proposed proved. an optimal control also established. Then, necessary optimality conditions are derived. As consequence, characterization given. Lastly, numerical results given show effectiveness strategy, which provides significant using AB in Caputo sense, comparing it classical integer one. The importance choosing very well order operators.</p>