An existence result for a new coupled system of differential inclusions involving with Hadamard fractional orders

Lili Zhang; Chengbo Zhai; Lili Zhang; Chengbo Zhai

doi:10.3934/era.2024301

Electronic Research Archive

2024, Volume 32, Issue 11: 6450-6466. doi: 10.3934/era.2024301

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Research article

An existence result for a new coupled system of differential inclusions involving with Hadamard fractional orders

Lili Zhang ¹,
Chengbo Zhai ^{1,2
,
,}

1.
School of Mathematics and Statistics, Shanxi University, Taiyuan 030006, China
2.
Key Laboratory of Complex Systems and Data Science of Ministry of Education, Shanxi University, Taiyuan 030006, China

Received: 03 September 2024 Revised: 22 October 2024 Accepted: 13 November 2024 Published: 26 November 2024

In this paper, we introduce a new coupled system of differential inclusions involving with Hadamard fractional orders. By applying a fixed point theorem for three operators containing $ x\in{AxBx+Cx} $ in Banach algebras, we get an existence result for the discussed system via multi-valued maps in a Banach space. An example is provided to support the validation of the theoretical result achieved.
- coupled system,
- differential inclusion,
- Hadamard fractional order,
- multi-valued maps,
- fixed-point theorem
Citation: Lili Zhang, Chengbo Zhai. An existence result for a new coupled system of differential inclusions involving with Hadamard fractional orders[J]. Electronic Research Archive, 2024, 32(11): 6450-6466. doi: 10.3934/era.2024301

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Abstract

In this paper, we introduce a new coupled system of differential inclusions involving with Hadamard fractional orders. By applying a fixed point theorem for three operators containing $ x\in{AxBx+Cx} $ in Banach algebras, we get an existence result for the discussed system via multi-valued maps in a Banach space. An example is provided to support the validation of the theoretical result achieved.

References

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