Positive Solutions to Fractional Boundary Value Problems with Nonlinear Boundary Conditions

Abstract

We consider a system of boundary value problems for fractional differential equation given byD0+βϕp(D0+αu)(t)=λ1a1(t)f1(u(t),v(t)),t∈(0,1),D0+βϕp(D0+αv)(t)=λ2a2(t)f2(u(t),v(t)),t∈(0,1), where1<α,β≤2,2<α+β≤4,λ1,λ2are eigenvalues, subject either to the boundary conditionsD0+αu(0)=D0+αu(1)=0,u(0)=0,D0+β1u(1)-Σi=1m-2a1i D0+β1u(ξ1i)=0,D0+αv(0)=D0+αv(1)=0,v(0)=0,D0+β1v(1)-Σi=1m-2a2i D0+β1v(ξ2i)=0orD0+αu(0)=D0+αu(1