Existence and stability of solution for multi-order nonlinear fractional differential equations

Leping Xie; Jueliang Zhou; Haiyun Deng; Yubo He; Leping Xie; Jueliang Zhou; Haiyun Deng; Yubo He

doi:10.3934/math.2022899

AIMS Mathematics

2022, Volume 7, Issue 9: 16440-16448. doi: 10.3934/math.2022899

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Existence and stability of solution for multi-order nonlinear fractional differential equations

1.
School of Mathematics and Computer Science, Huaihua University, Hunan 418000, China
2.
Key Laboratory of Intelligent Control Technology for Wuling-Mountain Ecological Agriculture in Hunan Province, Hunan 418000, China

Received: 13 April 2022 Revised: 20 June 2022 Accepted: 27 June 2022 Published: 07 July 2022
MSC : 26A33, 34A08, 34K20, 45D05

In this paper, relying on the Banach contraction mapping principle to discuss the existence of solution for a multi-order nonlinear fractional differential equations on the infinite interval $ [0, +\infty) $. Moreover the stability of Ulam-Hyers-Rassias and Ulam-Hyers to the initial value problem are obtained. An example that can illustrate the conclusions of this paper have been given at the end.
- multi-order nonlinear fractional differential equation,
- Banach contraction mapping principle,
- existence,
- stability
Citation: Leping Xie, Jueliang Zhou, Haiyun Deng, Yubo He. Existence and stability of solution for multi-order nonlinear fractional differential equations[J]. AIMS Mathematics, 2022, 7(9): 16440-16448. doi: 10.3934/math.2022899

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Abstract

In this paper, relying on the Banach contraction mapping principle to discuss the existence of solution for a multi-order nonlinear fractional differential equations on the infinite interval $ [0, +\infty) $. Moreover the stability of Ulam-Hyers-Rassias and Ulam-Hyers to the initial value problem are obtained. An example that can illustrate the conclusions of this paper have been given at the end.

References

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