Finite-time stability of mild solutions for Caputo-Katugampola fractional differential equations

Ni Zeng; Xiao-Hong Wu; Chuan-Yun Gu; Ni Zeng; Xiao-Hong Wu; Chuan-Yun Gu

doi:10.3934/era.2026171

Electronic Research Archive

2026, Volume 34, Issue 6: 3790-3803. doi: 10.3934/era.2026171

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Research article

Finite-time stability of mild solutions for Caputo-Katugampola fractional differential equations

1.
School of Science, Xihua University, Chengdu 610039, China
2.
School of Mathematics, Sichuan University of Arts and Science, Dazhou 635000, China

Received: 04 January 2026 Revised: 10 April 2026 Accepted: 23 April 2026 Published: 07 May 2026

This paper focuses on studying the existence and robust finite-time stability (FTS) for a more generalized class of nonlinear Caputo-Katugampola fractional differential equations with perturbation. The existence of mild solutions is proved by using the Sadovskii fixed-point theorem (SFPT). Then, sufficient conditions for robust FTS are obtained by applying the Jensen inequality and Hölder inequality. Finally, our theoretical results are supported by the research on the Lasota-Wazewska red blood cell (LWRBC) model.
- Caputo-Katugampola fractional differential equation,
- finite-time stability,
- Sadovskii fixed-point theorem,
- Jensen inequality,
- Grönwall inequality
Citation: Ni Zeng, Xiao-Hong Wu, Chuan-Yun Gu. Finite-time stability of mild solutions for Caputo-Katugampola fractional differential equations[J]. Electronic Research Archive, 2026, 34(6): 3790-3803. doi: 10.3934/era.2026171

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Abstract

This paper focuses on studying the existence and robust finite-time stability (FTS) for a more generalized class of nonlinear Caputo-Katugampola fractional differential equations with perturbation. The existence of mild solutions is proved by using the Sadovskii fixed-point theorem (SFPT). Then, sufficient conditions for robust FTS are obtained by applying the Jensen inequality and Hölder inequality. Finally, our theoretical results are supported by the research on the Lasota-Wazewska red blood cell (LWRBC) model.

References

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