This study investigates boundary value problems for nonlinear fractional differential equations. The differential operator is interpreted in the Hadamard sense and is coupled with a nonlinear term that involves the fractional derivative of the unknown function. The existence and multiplicity of positive solutions were established by a reducing-order technique based on the Guo–Krasnoselskii fixed-point theorem. Also, some examples are presented to illustrate the validity of our main results.