Existence of solutions of two-point boundary value problems for fractional p-Laplace differential equations at resonance

In this paper, we consider the following two-point boundary value problem for fractional p-Laplace differential equation where $D^{\alpha}_{0^{+}}$ , $D^{\beta}_{0^{+}}$ denote the Caputo fractional derivatives, 0<α,β≤1, 1<α+β≤2. By using the coincidence degree theory, a new result on the existence of solutions for above fractional boundary value problem is obtained. These results extend the corresponding ones of ordinary differential equations of integer order. Finally, an example is inserted to illustrate the validity and practicability of our main results.