含类分数阶Hukuhara导数集值积分微分方程的稳定性

doi:10.3969/j.issn.1000-1565.2023.01.001

河北大学学报(自然科学版) ›› 2023, Vol. 43 ›› Issue (1): 1-8.DOI: 10.3969/j.issn.1000-1565.2023.01.001

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含类分数阶Hukuhara导数集值积分微分方程的稳定性

王培光,毕佳慧,鲍俊艳

收稿日期:2022-04-25 出版日期:2023-01-25 发布日期:2023-02-22
通讯作者: 鲍俊燕(1978—)
作者简介:王培光(1963—),男,黑龙江哈尔滨人,河北大学教授,博士生导师,主要从事微分方程与控制理论的研究.
E-mail:pgwang@hbu.edu.cn
基金资助:
国家自然科学基金资助项目(12171135);河北省自然科学基金重点资助项目(A2020201021)

Stability of set-valued integral differential equations with fractional-like Hukuhara derivatives

WANG Peiguang, BI Jiahui, BAO Junyan

College of Mathematics and Information Science, Hebei University, Baoding 071002, China

Received:2022-04-25 Online:2023-01-25 Published:2023-02-22

摘要/Abstract

摘要： 讨论了一类特殊的集值积分微分方程的稳定性.通过类Lyapunov函数和比较原理,得到了一类特殊的方程解的等度稳定性、一致稳定性、等度渐近稳定性和严格稳定性准则.

关键词: 集值微分方程, 类分数阶Hukuhara导数, 广义Dini导数, 稳定性

Abstract: The stability of set-valued integral differential equations with fractional-like Hukuhara derivatives was investigated. The criteria of equistability, uniform stability, equiasymptotic stability and strictly stability of the solutions are obtained by using Lyapunov-like functions and the new comparison principle.

Key words: set-valued differential equations, fractional-like Hukuhara derivatives, generalized Dini derivatives, stability

中图分类号:

O175.13

王培光,毕佳慧,鲍俊艳. 含类分数阶Hukuhara导数集值积分微分方程的稳定性[J]. 河北大学学报(自然科学版), 2023, 43(1): 1-8.

WANG Peiguang, BI Jiahui, BAO Junyan. Stability of set-valued integral differential equations with fractional-like Hukuhara derivatives[J]. Journal of Hebei University(Natural Science Edition), 2023, 43(1): 1-8.

参考文献

[1] DIETHELM K. The analysis of fractional differential equations[M]. Cham: Springer International Publishing, 2004. DOI:10.1007/978-3-642-14574-2.
[2] PODLUBNY I. Fractional differential equations[M]. America: Lightning Source Inc, 1998.
[3] LAKSHMIKANTHAM V, LEELA S, SAMBANDHAM M. Lyapunov theory for fractional differential equations[J]. Commun Appl Anal, 2008, 12(4): 365-376.
[4] HRISTOVA S, TERSIAN S, TERZIEVA R. Lipschitz stability in time for Riemann-liouville fractional differential equations[J]. Fractal Fract, 2021, 5(2): 37. DOI: 10.3390/fractalfract5020037.
[5] AGARWAL R, HRISTOVA S, O’REGAN D. Lyapunov functions and strict stability of Caputo fractional differential equations[J].Adv Differ Equ, 2015, 2015(1): 1-20. DOI: 10.1186/s13662-015-0674-5.
[6] AGARWAL R, HRISTOVA S, O’REGAN D. A survey of Lyapunov functions, stability and impulsive caputo fractional differential equations[J].Fract Calc Appl Anal, 2016, 19(2): 290-318. DOI: 10.1515/fca-2016-0017.
[7] JANKOWSKI T. Fractional differential equations with causal operators[J]. Adv Differ Equ, 2015, 2015(1): 184. DOI: 10.1186/s13662-015-0528-1.
[8] BEN MAKHLOUF A, EL-HADY E S. Novel stability results for caputo fractional differential equations[J]. Math Probl Eng, 2021, 2021: 1-6. DOI: 10.1155/2021/9817668.
[9] STAMOVA I M. On the Lyapunov theory for functional differential equations of fractional order[J]. Proc Amer Math Soc, 2016, 144(4): 1581-1593. DOI: 10.1090/proc/12822.
[10] LAKSHMIKANTHAM V, BHASKAR T G, DEVI J V. Theory of set differential equations in metric spaces[M]. Cambridge, UK: Cambridge Scientific Publishers, 2006.
[11] MARTYNYUK A A. General properties of set-valued equations[M]. Cham: Springer International Publishing, 2019. DOI: 10.1007/978-3-030-07644-3_1.
[12] AHMAD B, SIVASUNDARAM S. Some stability results for set integro-differential equations[J]. Math Inequalities Appl, 2007(3): 597-605. DOI: 10.7153/mia-10-56.
[13] AHMAD B, SIVASUNDARAM S, ARABIA S. Setvalued perturbed hybrid integro-differential equations and stability in terms of two measures[J].Dynam sysl Appl,2007,16(2):232-256.
[14] MARTYNYUK A A, STAMOV G T, STAMOVA I M. Fractional-like Hukuhara derivatives in the theory of set-valued differential equations[J]. Chaos Solitons Fractals, 2020, 131: 109487. DOI: 10.1016/j.chaos.2019.109487.
[15] AGARWAL R, O'REGAN D, HRISTOVA S. Stability with initial time difference of caputo fractional differential equations by Lyapunov functions[J]. Z Anal Anwend, 2017, 36(1): 49-77. DOI: 10.4171/zaa/1579. (

含类分数阶Hukuhara导数集值积分微分方程的稳定性

Stability of set-valued integral differential equations with fractional-like Hukuhara derivatives

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