Positive Solution for Hadamard-Type Fractional Differential Equation with a Disturbance Parameter on Infinite Interval

This paper is concerned with Hadamard-type fractional boundary value problem involving a disturbance parameter on infinite interval. By applying the method of upper and lower solutions, Schauder fixed point theorem and fixed point index theory, we establish conditions for the existence, nonexistence, and multiplicity of positive solutions and show how the disturbance parameters influence the existence of positive solutions. Finally, an example is presented to illustrate our core results. Results of this paper extended and improved some existing results.