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arXiv · 1703.03336

Existence of solutions to fractional differential equations with three-point boundary conditions at resonance with general conditions

Bin-Bin He
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Abstract

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 $A^2\xi^{2\alpha-2}=A\xi^{\alpha-1}$ and $A^2\xi^{2\alpha-2}=I$ 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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Bin-Bin He. 2017-03-09. Existence of solutions to fractional differential equations with three-point boundary conditions at resonance with general conditions. https://arxiv.org/abs/1703.03336

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