Refinement of a Lyapunov-Type Inequality for a Fractional Differential Equation-Reference-Cited by-同舟云学术

Refinement of a Lyapunov-Type Inequality for a Fractional Differential Equation

Published:2024-07-23 Issue:8 Volume:16 Page:941
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Xiao Hongying¹,Li Zhaofeng²,Zhang Yuanyuan²,Liu Xiaoyou³

Affiliation:

1. Faculty of Science, Yibin University, Yibin 644000, China

2. Department of Mathematics, China Three Gorges University, Yichang 443002, China

3. School of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201, China

Abstract

In this paper, we focus on a fractional differential equation 0CDαu(t)+q(t)u(t)=0 with boundary value conditions u(0)=δu(1),u′(0)=γu′(1). The paper begins by pointing out the inadequacies of the study conducted by Ma and Yangin establishing Lyapunov-type inequalities. It then discusses the properties of its Green’s function and investigates extremum problems related to several linear functions. Finally, thorough classification and analysis of various cases for parameters δ and γ are conducted. As a result, a comprehensive solution corresponding to the Lyapunov-type inequality is obtained.

Funder

YiBin University

Publisher

MDPI AG

Link

https://www.mdpi.com/2073-8994/16/8/941/pdf

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