SOLVABILITY OF NONLOCAL HILFER FRACTIONAL MATRIX BOUNDARY VALUE PROBLEMS WITH $P$-LAPLACIAN AT RESONANCE IN $\mathbb{R}^N$

Fanmeng Meng; Weihua Jiang; Xian-Feng Zhou; Song Liu

doi:10.11948/20240112

2025 Volume 15 Issue 1

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Article navigation > Journal of Applied Analysis & Computation > 2025 > 15(1): 373-390

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Fanmeng Meng, Weihua Jiang, Xian-Feng Zhou, Song Liu. SOLVABILITY OF NONLOCAL HILFER FRACTIONAL MATRIX BOUNDARY VALUE PROBLEMS WITH $P$-LAPLACIAN AT RESONANCE IN $\mathbb{R}^N$[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 373-390. doi: 10.11948/20240112

Citation:

Fanmeng Meng, Weihua Jiang, Xian-Feng Zhou, Song Liu. SOLVABILITY OF NONLOCAL HILFER FRACTIONAL MATRIX BOUNDARY VALUE PROBLEMS WITH $P$-LAPLACIAN AT RESONANCE IN $\mathbb{R}^N$[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 373-390. doi: 10.11948/20240112

SOLVABILITY OF NONLOCAL HILFER FRACTIONAL MATRIX BOUNDARY VALUE PROBLEMS WITH $P$-LAPLACIAN AT RESONANCE IN $\mathbb{R}^N$

1.
School of Mathematical Sciences, Anhui University, Hefei 230601, China
2.
College of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, China

Author Bio: Email: mengfanmeng96@163.com(F. Meng); Email: jianghua64@163.com(W. Jiang); Email: liusong@ahu.edu.cn(S. Liu)
Corresponding author: Email: zhouxf@ahu.edu.cn(X.-F. Zhou)

Abstract

Abstract

In this paper, the solvability of boundary value problems for a class of nonlinear Hilfer fractional differential equations at resonance in $ \mathbb{R}^n $ is studied. In the past, research on matrix boundary value problems has consistently been conducted within the context of linear differential equations. The main contribution of this paper is the extension of linear problems to nonlinear ones. We begin by defining two Banach spaces endowed with appropriate norms and constructing suitable operators in these Banach spaces. Subsequently, by using the extension for the continuous theorem, certain sufficient conditions for the solvability of the problem are obtained. Finally, an example is provided to verify the effectiveness of our main results.
- Matrix boundary value problem /
- p-Laplacian /
- continuous theorem /
- Hilfer fractional derivative
MSC: 34A08, 34B15, 34A04, 34B10

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