A periodic boundary value problem of fractional differential equation involving $ p\left(t \right) $-Laplacian operator

Tingting Xue; Xiaolin Fan; Hong Cao; Lina Fu; Tingting Xue; Xiaolin Fan; Hong Cao; Lina Fu

doi:10.3934/mbe.2023205

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 3: 4421-4436. doi: 10.3934/mbe.2023205

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A periodic boundary value problem of fractional differential equation involving $ p\left(t \right) $-Laplacian operator

1.
School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi, Xinjiang, China
2.
College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang, China

Academic Editor: Feliz Manuel Barrão Minhós

Received: 27 October 2022 Revised: 03 December 2022 Accepted: 12 December 2022 Published: 23 December 2022

The purpose of this article is to research the existence of solutions for fractional periodic boundary value problems with $ p\left(t \right) $-Laplacian operator. In this regard, the article needs to establish a continuation theorem corresponding to the above problem. By applying the continuation theorem, a new existence result for the problem is obtained, which enriches existing literature. In addition, we provide an example to verify the main result.
- fractional differential equation,
- boundary value problem,
- $ p\left(t \right) $-Laplacian operator,
- continuation theorem
Citation: Tingting Xue, Xiaolin Fan, Hong Cao, Lina Fu. A periodic boundary value problem of fractional differential equation involving $ p\left(t \right) $-Laplacian operator[J]. Mathematical Biosciences and Engineering, 2023, 20(3): 4421-4436. doi: 10.3934/mbe.2023205

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Abstract

The purpose of this article is to research the existence of solutions for fractional periodic boundary value problems with $ p\left(t \right) $-Laplacian operator. In this regard, the article needs to establish a continuation theorem corresponding to the above problem. By applying the continuation theorem, a new existence result for the problem is obtained, which enriches existing literature. In addition, we provide an example to verify the main result.

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