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We investigate new results about Lyapunov-type inequality by considering a fractional boundary value problem subject to mixed boundary conditions. We give a necessary condition for nonexistence of solutions for a class of boundary value problems involving Riemann-Liouville fractional order. The order considered here is 3 < α ≤ 4. The investigation is based on a construction of Green's function and on finding its corresponding maximum value. In order to illustrate the result, we provide andoi:10.22436/jnsa.009.05.27 fatcat:j3psi3b5xzbohmxeklbuxaka5e