Positive solutions for nonlinear fractional differential equations with a disturbance parameter on an infinite interval

Abstract

This paper studies a class of integral boundary value problems of fractional differential equations with a disturbance parameter on an infinite interval. By applying the upper-lower solution method and fixed point index theory, the influence of the disturbance parameter on the existence of positive solutions is rigorously analyzed. Sufficient conditions for the existence of no positive solution, at least one positive solution, and at least two positive solutions are established. An example is provided to validate the results. The results of this study provide a significant complement and refinement to some existing findings.