Existence and uniqueness of solutions for a class of initial value problems of fractional differential systems on half lines

In this article, we establish the existence and uniqueness results for solutions of a class of initial value problems of nonlinear fractional differential systems on half lines involving Riemann–Liouville fractional derivatives. Our analysis relies on the well-known fixed point theorem of Schauder. The novelty of this paper is that the problems discussed are defined on half lines, and the nonlinearities f and g   are allowed to be singular functions. Furthermore, we allow p∈(0,β)$p\in (0,\beta )$ and q∈(0,α)$q\in (0,\alpha )$.