This paper establishes the existence of unique and multiple solutions to two nonlocal equations with fractional operators. The main results are obtained using the variational method and algebraic analysis. The conclusion is that there exists a constant ${\lambda }^{*}>0$ such that the equations have only three, two, and one solution, respectively, for $\lambda \in (0,{\lambda }^{*})$, $\lambda ={\lambda }^{*}$, and $\lambda >{\lambda }^{*}$. The main conclusions fill the gap in the knowledge of this kind of fractional-order problem.