Superconductivity and magnetism were previously thought as incompatible until the discoveryrnof some rare earth ternary compounds that show the coexistence of superconductivityrnand magnetism. In some of the recently discovered iron-based layered superconductors,rnsuperconductivity and magnetism coexist. In the present work we examine thernpossibility of coexistence of antiferromagnetism and superconductivity in samarium arsenidernoxide superconductor (SmAsO1À€€xFxFe). Using a model of the Hamiltonian andrnretarded double time Greens function formalism, we found expressions for superconductingrntransition temperature (Tc), superconductivity order parameter ( sc(T)), AFM orderrnparameter ( ), and AFM transition temperature (Tm). We obtained the phase diagramsrn(Tcvs ) and (Tmvs ) to obtain the region where both orders ,i.e, superconductivity andrnAFM coexist. The region under the intersection of the two merged graphs shows thatrnsuperconductivity and AFM coexist in the system(SmAsO1ð€€€xFxFe)