一类具有瞬时和非瞬时脉冲的 $\psi$-Caputo 型分数阶微分方程的多解性

Abstract

Abstract:

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 involving $\psi$-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 when $\mu\in \mathbb{R}$. 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.

Key words: $\psi$-Caputo fractional derivative, fractional differential equation, variational methods, Three critical point theorems

CLC Number:

O177.91

Yao Wangjin, Zhang Huiping. Multiple Solutions for a Class of $\psi$-Caputo-Type Fractional Differential Equations with Instantaneous and Non-Instantaneous Impulses[J].Acta mathematica scientia,Series A, 2025, 45(3): 807-823.

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References 30

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Multiple Solutions for a Class of $\psi$-Caputo-Type Fractional Differential Equations with Instantaneous and Non-Instantaneous Impulses

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