Existence of solutions for fractional differential equations with three-point boundary conditions at resonance in $\mathbb{R}^n$

Abstract

In this paper, by applying the coincidence degree theory which was first introduced by Mawhin, we obtain an existence result for the fractional three-point boundary value problems in $\mathbb{R}^n$, where the dimension of the kernel of fractional differential operator with the boundary conditions can take any value in $\{1,2,\ldots,n\}$. This is our novelty. Several examples are presented to illustrate the result