On the existence of solutions for multi-term $ p $-Laplacian fractional differential equations with anti-periodic boundary conditions

Wei Zhang; Feiyan Xie; Jinbo Ni; Wei Zhang; Feiyan Xie; Jinbo Ni

doi:10.3934/era.2026161

Electronic Research Archive

2026, Volume 34, Issue 5: 3593-3610. doi: 10.3934/era.2026161

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Research article

On the existence of solutions for multi-term $ p $-Laplacian fractional differential equations with anti-periodic boundary conditions

School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan 232001, China

Received: 05 March 2026 Revised: 13 April 2026 Accepted: 17 April 2026 Published: 27 April 2026

This paper investigates the anti-periodic boundary value problem for multi-term fractional differential equations that involve the $ p $-Laplacian operator. We establish existence results by separately applying the Leray-Schauder nonlinear alternative and the Krasnosel'skii's fixed point theorem. Finally, two illustrative examples are presented to demonstrate the effectiveness of the main results.
- multi-term fractional differential equation,
- anti-periodic boundary condition,
- fixed point theorem,
- existence
Citation: Wei Zhang, Feiyan Xie, Jinbo Ni. On the existence of solutions for multi-term $ p $-Laplacian fractional differential equations with anti-periodic boundary conditions[J]. Electronic Research Archive, 2026, 34(5): 3593-3610. doi: 10.3934/era.2026161

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Abstract

This paper investigates the anti-periodic boundary value problem for multi-term fractional differential equations that involve the $ p $-Laplacian operator. We establish existence results by separately applying the Leray-Schauder nonlinear alternative and the Krasnosel'skii's fixed point theorem. Finally, two illustrative examples are presented to demonstrate the effectiveness of the main results.

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