A study of existence and multiplicity of positive solutions for nonlinear fractional differential equations with nonlocal boundary conditions

This paper deals with the existence, uniqueness and the multiplicity for the boundary value problem of a class of fractional differential equations involving the Riemann-Liouville fractional derivative with nonlocal integral boundary conditions. By using the properties of the Green's function, the Banach contraction principle, the xed point index theory and the Leggett-Williams fixed point theorem, one shows the existence and the uniqueness of positive solutions and the existence and multiplicity of positive solutions. As applications, some examples are presented at the end to illustrate the main results.