Existence and uniqueness of positive solutions for nonlinear fractional mixed problems

Abstract This paper is devoted to study the existence and uniqueness of solutions a one parameter family nonlinear Riemann–Liouville fractional differential equations with mixed boundary value conditions. An exhaustive sign related Green’s function carried out. Under suitable assumptions on asymptotic behavior part equation at zero infinity, by application fixed point theory compact operators defined in cones, it proved that there exists least solution considered problem. Moreover, method lower upper developed deduced combination both techniques. In particular cases, Banach contraction principle used ensure solutions.