  Using the new conformable fractional derivative, which differs from the
Riemann-Liouville and Caputo fractional derivatives, we reformulate the
second-order conjugate boundary value problem in this new setting. Utilizing
the corresponding positive fractional Green's function, we apply a functional
compression-expansion fixed point theorem to prove the existence of a positive
solution. We then compare our results favorably to those based on the
Riemann-Liouville fractional derivative.
