Nonexistence and uniqueness of positive solutions to a nonlinear fractional p-Laplacian system

This paper investigates the nonexistence and uniqueness of positive solutions to a kind of two-point boundary value problem (BVP) for nonlinear fractional differential equations with p-Laplacian operator, and presents a number of new results. First, the considered BVP is converted to an operator equation by using the property of Caputo derivative. Second, based on the operator equation and some fixed point theorems, several sufficient conditions are presented for the nonexistence and the uniqueness of positive solutions. Finally, several illustrative examples are given to support the obtained new results. The study of illustrative examples shows that the obtained results are applicable.