Existence of solutions to fractional differential equations with three-point boundary conditions at resonance with general conditions
This paper presents a new technique to investigate the existence of solutions to fractional three-point boundary value problems at resonance in a Hilbert space. Based on the proposed method, the restricted conditions $A^2ξ^{2α-2}=Aξ^{α-1}$ and $A^2ξ^{2α-2}=I$ on the operator $A$, which have been used in \cite{Zhou2}, are removed. It is shown that the system under consideration admits at least one solution by applying coincidence degree theory. Finally, an illustrative example is presented.
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