Existence and multiplicity of positive solutions for singular fractional boundary value problems

In this paper, we discuss the existence and multiplicity of positive solutions for the singular fractional boundary value problem D0+αu(t)+f(t,u(t),D0+νu(t),D0+μu(t))=0,u(0)=u′(0)=u″(0)=u″(1)=0,u(0)=u′(0)=u″(0)=u″(1)=0, where 3<α≤43<α≤4, 0<ν≤10<ν≤1, 1<μ≤21<μ≤2, D0+α is the standard Riemann–Liouville fractional derivative, ff is a Carathédory function and f(t,x,y,z)f(t,x,y,z) is singular at the value 0 of its arguments x,y,zx,y,z. By means of a fixed point theorem, the existence and multiplicity of positive solutions are obtained.