Open AccessNew Lyapunov-type inequalities for fractional multi-point boundary value problems involving Hilfer-Katugampola fractional derivative
Author(s) -
Wei Zhang,
Jifeng Zhang,
Jinbo Ni
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022064
Subject(s) - mathematics , fractional calculus , lyapunov function , contraction principle , boundary value problem , mathematical analysis , fixed point theorem , type (biology) , fixed point , nonlinear system , physics , ecology , quantum mechanics , biology
In this paper, we present new Lyapunov-type inequalities for Hilfer-Katugampola fractional differential equations. We first give some unique properties of the Hilfer-Katugampola fractional derivative, and then by using these new properties we convert the multi-point boundary value problems of Hilfer-Katugampola fractional differential equations into the equivalent integral equations with corresponding Green's functions, respectively. Finally, we make use of the Banach's contraction principle to derive the desired results, and give a series of corollaries to show that the current results extend and enrich the previous results in the literature.