Results on system of Atangana–Baleanu fractional order Willis aneurysm and nonlinear singularly perturbed boundary value problems

Abstract

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.