Theoretical and semi-analytical results to a biological model under Atangana–Baleanu–Caputo fractional derivative

This manuscript is related to finding a solution of the SIR model under Mittag-Leffler type derivative. For the required results, we use Laplace transform together with Adomian decomposition method (LADM). The mentioned method is a powerful tool to deal with various linear and nonlinear problems of “fractional order differential equations (FODEs)”. Also, we study some results devoted to qualitative theory for the concerned model. Computational results show the verification of the established analysis. Briefly, we state that qualitative theory for the existence of solution is important to ensure whether the considered problem has a solution or not. Further ensuring the existence of solution, we investigate approximate solution which is computed in the form of infinite series. The results are graphically displayed to analyze the adopted procedure for solving nonlinear FODEs under ABC derivative.