Lyapunov-Type Inequalities for a Fractional Boundary Value Problem with a Fractional Boundary Condition

Abstract: In this paper, we consider a linear fractional differential equation with fractional boundary conditions. First, by obtaining Green's function, we derive the Lyapunov-type inequalities for such boundary value problems. Furthermore, we use the contraction mapping theorem to study the existence of a unique solution to a nonlinear problem.