Existence of concave positive solutions for nonlinear fractional differential equation with \(p\)-Laplacian operator (Q6159701)

The authors study the existence and multiplicity of concave positive solutions for a boundary value problem for two-sided third-order fractional differential equations involving the Caputo derivative. Using the Leggett-Williams fixed point theorem, the existence of at least three solutions are obtained. Some examples are provided to illustrate applications of the results. Reviewer's remark: Lemmas 2.6 and 2.7, which are not proved in this paper, are used to prove one of the main results: Lemma 2.13. The reviewer believes that the two results are incomplete and some additional conditions need to be imposed.