Sharp estimates for the unique solution of two-point fractional-order boundary value problems

In this short note, we derive a sharp condition in terms of the end-points of the given interval which ensures the uniqueness of solutions for a Liouville-Caputo type fractional differential equation supplemented with two-point boundary conditions. A comparison with Riemann-Liouville type two-point fractional boundary value problem as well as with the classical two-point problem is presented.