An Erdélyi-Kober fractional coupled system: Existence of positive solutions

Mengjiao Zhao; Chen Yang; Mengjiao Zhao; Chen Yang

doi:10.3934/math.2024247

AIMS Mathematics

2024, Volume 9, Issue 2: 5088-5109. doi: 10.3934/math.2024247

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Research article

An Erdélyi-Kober fractional coupled system: Existence of positive solutions

Mengjiao Zhao ¹,
Chen Yang ^{2
,
,}

1.
School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China
2.
Shanxi Vocational University of Engineering Science and Technology, Taiyuan, Shanxi 030619, China

Received: 21 October 2023 Revised: 29 December 2023 Accepted: 02 January 2024 Published: 24 January 2024
MSC : 26A33, 34A37, 34B15

This paper studies an Erdélyi-Kober fractional coupled system where the variable is in an infinite interval, and the existence of positive solutions is considered. We first give proper conditions and then use the Guo-Krasnosel'skii fixed point theorem to discuss our problem in a special Banach space. The monotone iterative technique and the existence results of positive solutions for this system are established naturally. To show the plausibility of our main results, several concrete examples are given at the end.
- Erdélyi-Kober type fractional derivative,
- fractional coupled system,
- infinite interval,
- monotone iterative technique,
- positive solution
Citation: Mengjiao Zhao, Chen Yang. An Erdélyi-Kober fractional coupled system: Existence of positive solutions[J]. AIMS Mathematics, 2024, 9(2): 5088-5109. doi: 10.3934/math.2024247

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Abstract

This paper studies an Erdélyi-Kober fractional coupled system where the variable is in an infinite interval, and the existence of positive solutions is considered. We first give proper conditions and then use the Guo-Krasnosel'skii fixed point theorem to discuss our problem in a special Banach space. The monotone iterative technique and the existence results of positive solutions for this system are established naturally. To show the plausibility of our main results, several concrete examples are given at the end.

References

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