This article concerning to initiate the existence of solutions via fixed point technique for:1.The Atangana–Baleanu Willis Aneurysm System {0ABDtn1p=q0ABDtn2q=Fcos(wt)−ψq−ap+bp2−cp3wheren1>0,n2<2.2.Singular perturbations of boundary value problems for non- linear fuzzy differential equations of the second order {ϵU″(p)=Θ(p,U(p),U′(p));0<p<1withU(0)=θ1U(1)=θ2 where θ1,θ2∈I, here I=[0,1],ϵ represents a small parameter and Θ:I×M×M→F(M) is a smooth function. The Atangana–Baleanu Willis Aneurysm System {0ABDtn1p=q0ABDtn2q=Fcos(wt)−ψq−ap+bp2−cp3wheren1>0,n2<2. Singular perturbations of boundary value problems for non- linear fuzzy differential equations of the second order {ϵU″(p)=Θ(p,U(p),U′(p));0<p<1withU(0)=θ1U(1)=θ2 where θ1,θ2∈I, here I=[0,1],ϵ represents a small parameter and Θ:I×M×M→F(M) is a smooth function.