VARIATIONAL APPROACH TO MIXED BOUNDARY VALUE PROBLEMS OF FRACTIONAL STURM-LIOUVILLE DIFFERENTIAL EQUATIONS WITH INSTANTANEOUS AND NON-INSTANTANEOUS IMPULSES

Zhongyuan Wang; Wei Zhang; Jinbo Ni

doi:10.11948/20240278

2025 Volume 15 Issue 2

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Zhongyuan Wang, Wei Zhang, Jinbo Ni. VARIATIONAL APPROACH TO MIXED BOUNDARY VALUE PROBLEMS OF FRACTIONAL STURM-LIOUVILLE DIFFERENTIAL EQUATIONS WITH INSTANTANEOUS AND NON-INSTANTANEOUS IMPULSES[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 1113-1133. doi: 10.11948/20240278

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Zhongyuan Wang, Wei Zhang, Jinbo Ni. VARIATIONAL APPROACH TO MIXED BOUNDARY VALUE PROBLEMS OF FRACTIONAL STURM-LIOUVILLE DIFFERENTIAL EQUATIONS WITH INSTANTANEOUS AND NON-INSTANTANEOUS IMPULSES[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 1113-1133. doi: 10.11948/20240278

VARIATIONAL APPROACH TO MIXED BOUNDARY VALUE PROBLEMS OF FRACTIONAL STURM-LIOUVILLE DIFFERENTIAL EQUATIONS WITH INSTANTANEOUS AND NON-INSTANTANEOUS IMPULSES

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 (2208085QA05)

Abstract

Abstract

This paper investigates a class of fractional Sturm-Liouville differential equations with mixed boundary conditions, which are subjected to parameter and impulsive perturbations (including instantaneous and non-instantaneous impulses). By employing the variational methods and critical point theorems, we derive several criteria that guarantee the existence of at least one and two classical solutions, respectively, when the parameters fall within different intervals. Furthermore, we provide an example to demonstrate the effectiveness of our main results.
- Fractional Sturm-Liouville equation /
- mixed boundary condition /
- instantaneous impulse /
- non-instantaneous impulse /
- existence and multiplicity of solution /
- critical point theorem
MSC: 34A08, 34B08, 34B15, 34B37

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References

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