VARIATIONAL METHOD TO THE FRACTIONAL IMPULSIVE EQUATION WITH NEUMANN BOUNDARY CONDITIONS

Wei Zhang; Zhongyuan Wang; Jinbo Ni

doi:10.11948/20230464

2024 Volume 14 Issue 5

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Wei Zhang, Zhongyuan Wang, Jinbo Ni. VARIATIONAL METHOD TO THE FRACTIONAL IMPULSIVE EQUATION WITH NEUMANN BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 2890-2902. doi: 10.11948/20230464

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Wei Zhang, Zhongyuan Wang, Jinbo Ni. VARIATIONAL METHOD TO THE FRACTIONAL IMPULSIVE EQUATION WITH NEUMANN BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 2890-2902. doi: 10.11948/20230464

VARIATIONAL METHOD TO THE FRACTIONAL IMPULSIVE EQUATION WITH NEUMANN BOUNDARY CONDITIONS

School of mathematics and big data, Anhui University of Science and Technology, Huainan, Anhui 232001, China

Author Bio: Email: zywang_equations@163.com(Z. Wang); Email: nijinbo2005@126.com(J. Ni)
Corresponding author: Email: zhangwei_azyw@163.com(W. Zhang)
Fund Project: The authors were supported by Anhui Provincial Natural Science Foundation (2208085MA04, 2208085QA05) and National Natural Science Foundation of China (11601007)

Abstract

Abstract

We study the multiplicity of solutions for a class of fractional differential equations influenced by both instantaneous and non-instantaneous impulses, subject to Neumann boundary conditions. A key contribution of this paper is that we have established a new variational structure and successfully applied critical point theory to investigate the impulsive fractional Neumann boundary value problem. By using the critical point theorem, we give some new criteria to guarantee that the impulsive problem has at least three solutions. An example is also given to illustrate the main results.
- Fractional differential equation /
- Neumann boundary condition /
- critical point theorem /
- instantaneous impulses /
- non-instantaneous impulses
MSC: 34A08, 34B15, 34B37

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References

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