A boundary value problem for fractional differential equation with pp-Laplacian operator at resonance

In this paper, by using the coincidence degree theory, we consider the following boundary value problem for fractional pp-Laplacian equation {D0+βϕp(D0+αx(t))=f(t,x(t),D0+αx(t)),t∈[0,1],D0+αx(0)=D0+αx(1)=0, where 0<α,β≤1,1<α+β≤2, D0+α is a Caputo fractional derivative, and p>1p>1, ϕp(s)=|s|p−2sϕp(s)=|s|p−2s is a pp-Laplacian operator. A new result on the existence of solutions for the above fractional boundary value problem is obtained, which generalize and enrich some known results to some extent from the literature.