Lyapunov-type inequalities for sequential fractional boundary value problems using Hilfer’s fractional derivative

Abstract

Abstract This paper is devoted to studying the Lyapunov-type inequality for sequential Hilfer fractional boundary value problems. We first provide some properties of Hilfer fractional derivative, and then establish Lyapunov-type inequalities for a sequential Hilfer fractional differential equation with two types of multi-point boundary conditions. Our results generalize and compliment the existing results in the literature.

Keywords

• Lyapunov-type inequality
• Sequential fractional differential equation
• Hilfer fractional derivative
• Multi-point boundary condition