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Research Article | Open Access

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

Leping Xie1, Jueliang Zhou1,2, Haiyun Deng1,2, Yubo He1,2( )
School of Mathematics and Computer Science, Huaihua University, Hunan 418000, China
Key Laboratory of Intelligent Control Technology for Wuling-Mountain Ecological Agriculture in Hunan Province, Hunan 418000, China
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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 , + ∞ ). 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.

Keywords

multi-order nonlinear fractional differential equationBanach contraction mapping principleexistencestability
CLC number: 26A33, 34A08, 34K20, 45D05

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 16440-16448
DOI: 10.3934/math.2022899

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Cite this article:
Xie L, Zhou J, Deng H, et al. Existence and stability of solution for multi-order nonlinear fractional differential equations. AIMS Mathematics, 2022, 7(9): 16440-16448. https://doi.org/10.3934/math.2022899

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Received: 13 April 2022
Revised: 20 June 2022
Accepted: 27 June 2022
Published: 15 September 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)