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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.

In this paper, we investigate the existence of solutions for multi-point boundary value problems at resonance concerning fractional differential equation on a half-line. Our analysis relies on the coincidence degree of Mawhin. As an application, an example is presented to illustrate the main results. 2010 Mathematics Subject Classification. 34A08; 34B10; 34B40.