positive solutions for a class of fractional boundary value problem with changing sign nonlinearity

in this paper, we discuss the existence of positive solutions to the following fractional boundary value problem with changing sign nonlinearity.

{d^α₀₊u(t) + λf (t, u(t)) = 0, 0 < t < 1,

u(0) = u′(0) = u(1) = 0,

where 2 < α ≤ 3 is a real number, d^α₀₊ is the standard riemann–liouville derivative, λ is a positive parameter, f may change sign and may be singular at t = 0, 1.