Positive solutions for semipositone singular α-order (2< α <3) fractional BVPs on the half-line with D^β-derivative dependence

. This article deals with existence of positive solutions to the fractional boundary value where α ∈ ( 2 , 3 ) , β ∈ ( 0 , α − 2 ] , D α is the standard Riemann-Liouville fractional derivative and the function f : ( 0 , + ∞ ) 3 → R is continuous semipositone and may exhibit singular at u = 0 and at D β u = 0 The main existence result is obtained by means of Guo-Krasnoselskii’s version of expansion and compression of a cone principal in a Banach space.