Solvability of fractional differential equations with integral boundary conditions at resonance

Abstract

By using the coincidence degree theory due to Mawhin and constructing suitable operators, some sufficient conditions for the existence of solution for a class of fractional differential equations with integral boundary conditions at resonance are established, which are complement of previously known results. The interesting point is that we shall deal with the case $\text{\rm dim}\text{\rm Ker}L=2$, which will cause some difficulties in constructing the projector $Q$. An example is given to illustrate our result.