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

Abstract In this paper, by using the coincidence degree theory, we consider the following boundary value problem for fractional p -Laplacian equation { D 0 + β ϕ p ( D 0 + α x ( t ) ) = f ( t , x ( t ) , D 0 + α x ( t ) ) , t ∈ [ 0 , 1 ] , D 0 + α x ( 0 ) = D 0 + α x ( 1 ) = 0 , where 0 α , β ≤ 1 , 1 α + β ≤ 2 , D 0 + α is a Caputo fractional derivative, and p > 1 , ϕ p ( s ) = | s | p − 2 s is a p -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.