Lyapunov inequality for a Caputo fractional differential equation with Riemann–Stieltjes integral boundary conditions

Abstract

In this a Lyapunov‐type inequality is obtained for the fractional differential equation with Caputo derivative together with the boundary conditions where are functions of bounded variation, , and are nonnegative constants, and is a continuous function. We have divided the Greens function of this problem into two parts, and their upper bounds are obtained separately in order to obtain our results. The classical celebrated result of Lyapunov has become a consequence of our result.