Acta mathematica scientia,Series A ›› 2025, Vol. 45 ›› Issue (3): 807-823.

Previous Articles     Next Articles

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

Wangjin Yao1(),Huiping Zhang2,*()   

  1. 1Fujian Key Laboratory of Financial Information Processing, Putian University, Fujian Putian 351100
    2School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117
  • Received:2024-05-07 Revised:2024-11-27 Online:2025-06-26 Published:2025-06-20
  • Supported by:
    Natural Science Foundation of Fujian Province(2023J01994);Natural Science Foundation of Fujian Province(2023J01995);Natural Science Foundation of Fujian Province(2024J01871);Natural Science Foundation of Fujian Province(2024J01873);Program for Innovative Research Team in Science and Technology in Fujian Province University(2018-39);Fujian Alliance of Mathematics(2024SXLMMS05);Education and Research Project for Middle and Young Teachers in Fujian Province(JAT231093)

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 ψ-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 μR. 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: ψ-Caputo fractional derivative, fractional differential equation, variational methods, Three critical point theorems

CLC Number: 

  • O177.91
Trendmd