Lyapunov-type inequality for a higher order dynamic equation on time scales

The purpose of this work is to establish a Lyapunov-type inequality for the following dynamic equation [Formula: see text]on some time scale T under the anti-periodic boundary conditions [Formula: see text], where [Formula: see text] for [Formula: see text] and [Formula: see text], [Formula: see text] with [Formula: see text] and [Formula: see text], p is the quotient of two odd positive integers and [Formula: see text] with [Formula: see text].