An existence and uniqueness result for linear fractional impulsive boundary value problems as an application of Lyapunov type inequality

Abstract

A new and different approach to the investigation of the existence and uniqueness of solution of nonhomogenous impulsive boundary value problems involving the Caputo fractional derivative of order  $\alpha$ ($1<\alpha\leq 2$) is brought by using Lyapunov type inequality. To express and to analyze the unique solution, Green's function and its bounds are established, respectively. As far as we know, this approach based on the link between fractional boundary value problems and Lyapunov type inequality, has not been revealed even in the absence of impulse effect. Besides, the novel Lyapunov type inequality generalizes the related ones in the literature.