Solvability of Fractional Differential Equation with Nonlocal Boundary Conditions at Resonance

Abstract

By using the Mawhin’s continuation theorem, we establish a sufficient condition for the existence of at least one solution of a boundary value problem for differential equation of fractional order. The new point is that we proved Fredholm property of the differential operator directly without going through the construction of projectors. Moreover, our work shows the way to construct the general continuous projector Q for both two cases of \(\dim \mathrm {K}\mathrm {e}\mathrm {r}\,L \in \{1, 2\}\).