Unbounded solutions to a boundary value problem of fractional order on the half-line

This paper deals with a boundary value problem of a fractional differential equation with the nonlinear term dependent on a fractional derivative of lower order on the semi-infinite interval. An appropriate compactness criterion is established, such that we can use Schauder’s fixed point theorem on an unbounded domain to obtain the existence result for solutions. Moreover, a suitable choice of a Banach space allows the solutions to be unbounded. An example illustrating our main result is also given.