The aim of the present paper is to investigate the existence and nonexistence of solutions for a nonlinear Erdélyi-Kober (EK) fractional-order differential equation associated with EK fractional integral boundary conditions on the half-line. The considered equation contains a large amount of linear and nonlinear differential equations withEK fractional operator. In order to consider this equation, we first formulated the linear problem in integral equation. Our approach is based on recent fixed point theorem which uses the strongly positive-like operators and eigenvalue criteria for existence and nonexistence of positive solutions
