Lyapunov inequality for a class of fractional differential equations with Dirichlet boundary conditions

In this paper we present Lyapunov inequality for the following fractional boundary value problem { d / dt (1/2a Dt - β u (t)+1/2t Db - β u (t) ) + ω(t)u(t) = 0, a t b, u(a) = u(b) = 0, where aD−β and tD−β are the left and right Riemann-Liouville fractional integrals of order 0 ≤ β 1, respectively, and ω ∈ L^1([a, b], R). Using the obtained inequality, we provide lower bounds for the first eigenvalue of the fractional differential equations with homogeneous Dirichlet boundary problem.