摘要
作为整数阶微分方程的推广,分数阶微分方程近年来是一个十分热门的研究对象.分数阶微分方程在反常扩散、流体流动、流行病学和粘弹性力学等许多科学与工程实际问题的建模中发挥着重要作用.该文研究一类包含ψ-Caputo分数阶导数和具有瞬时和非瞬时脉冲的分数阶微分方程.当参数μ∈R时,利用变分方法和两类三临界点定理,获得至少三个古典解的存在性.并且,该文改进和推广了最近的一些结果.最后,给出两个例子来验证所得结果的可行性和有效性.
In recent years,as an extension of integer-order differential equations,fractional differential equations have became a popular research object.They play an important role in modeling many practical problems of science and engineering,such as anomalous diffusion,fluid flow,epidemiology,viscoelastic mechanics,etc.In this paper,a class of fractional differential equation involvingψ-Caputo fractional derivative with instantaneous and non-instantaneous impulses is considered.By using variational methods and two types of three critical point theorems,the existence of at least three classical solutions is obtained whenμ∈R.Moreover,some recent results are improved and extended.In the end,two examples are given to verify the feasibility and effectiveness of the obtained results.
作者
姚旺进
张慧萍
Wangjin Yao;Huiping Zhang(Fujian Key Laboratory of Financial Information Processing,Putian University,Fujian Putian 351100;School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117)
出处
《数学物理学报(A辑)》
北大核心
2025年第3期807-823,共17页
Acta Mathematica Scientia
基金
福建省自然科学基金(2023J01994,2023J01995,2024J01871,2024J01873)
福建省高校创新团队培育计划(2018-39)
福建省高校数学学科联盟科研项目(2024SXLMMS05)
福建省中青年教师教育科研项目(JAT231093)。
关键词
ψ-Caputo分数阶导数
分数阶微分方程
变分方法
三临界点定理
ψ-Caputo fractional derivative
fractional differential equation
variational methods
Three critical point theorems
