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 semiinfinite 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.