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AIMS Mathematics

2024, Volume 9, Issue 6: 15132-15148. doi: 10.3934/math.2024734
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Research article

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

  • 1.
    School of Science, Hubei University of Technology, Wuhan 430068, China
  • 2.
    School of Mathematics, Sun Yat-Sen University, Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, China
  • Received: 25 January 2024 Revised: 31 March 2024 Accepted: 07 April 2024 Published: 26 April 2024

  • MSC : 39A12, 39A70

  • 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.

    Citation: Mei Wang, Baogua Jia. Finite-time stability and uniqueness theorem of solutions of nabla fractional $ (q, h) $-difference equations with non-Lipschitz and nonlinear conditions[J]. AIMS Mathematics, 2024, 9(6): 15132-15148. doi: 10.3934/math.2024734

    Related Papers:

  • 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.


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