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Research Article | Open Access

Finite-time stability and uniqueness theorem of solutions of nabla fractional ( q , h )-difference equations with non-Lipschitz and nonlinear conditions

Mei Wang1( ), Baogua Jia2
School of Science, Hubei University of Technology, Wuhan 430068, China
School of Mathematics, Sun Yat-Sen University, Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, China
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Abstract

In this paper, the discrete ( q , h )-fractional Bihari inequality is generalized. On the grounds of inequality, the finite-time stability and uniqueness theorem of solutions of ( q , h )-fractional difference equations with non-Lipschitz and nonlinear conditions is concluded. In addition, the validity of our conclusion is illustrated by a nonlinear example with a non-Lipschitz condition.

Keywords

fractional (q, h)-difference equationfinite-time stabilityuniquenessnon-Lipschitz conditiondiscrete (q, h)-fractional Bihari inequality
CLC number: 39A12, 39A70

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AIMS Mathematics
Volume 9 Issue 6,
May 2024
Pages 15132-15148
DOI: 10.3934/math.2024734

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Cite this article:
Wang M, Jia B. Finite-time stability and uniqueness theorem of solutions of nabla fractional ( q , h )-difference equations with non-Lipschitz and nonlinear conditions. AIMS Mathematics, 2024, 9(6): 15132-15148. https://doi.org/10.3934/math.2024734

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Received: 25 January 2024
Revised: 31 March 2024
Accepted: 07 April 2024
Published: 26 April 2024
©2024 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)