Lyapunov-type inequalities for fractional multi-point boundary value problems using a new generalized fractional derivative

Abstract

In this paper, we present a new class of fractional derivative (bi-order Hilfer-Katugampola fractional derivative). In the framework of this type of fractional calculus, we discuss a class of fractional multi-point boundary value problems (BVPs) and obtain some new fractional Lyapunov-type inequalities. Based on the generality of the definition of bi-order Hilfer-Katugampola fractional derivative, we provide a series of corollaries, which demonstrate that our results unify and generalize some known results in the existing literature.