Mittag-Leffler-Ulam stabilities for variable fractional-order differential equations driven by Lévy noise

被引：0

作者：

Moualkia, Seyfeddine ^{[1
,3
]}

Liu, Yang ^{[1
,2
]}

Qiu, Jianlong ^{[4
]}

Cao, Jinde ^{[5
]}

机构：

[1] Zhejiang Normal Univ, Sch Math Sci, Jinhua 321004, Peoples R China

[2] Yili Normal Univ, Sch Math & Stat, Yining 835000, Peoples R China

[3] Univ 8 May 1945, Dept Math, Guelma 24000, Algeria

[4] Linyi Univ, Sch Automat & Elect Engn, Linyi 276005, Peoples R China

[5] Southeast Univ, Sch Math, Nanjing 210096, Peoples R China

来源：

NONLINEAR DYNAMICS | 2025年

关键词：

Stochastic differential equations; L & eacute; vy noise; Variable fractional-order; Mittag-Leffler-Ulam stability;

D O I：

10.1007/s11071-024-10859-6

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

This paper is devoted to investigating the existence and uniqueness of solutions, as well as Mittag-Leffler-Ulam stabilities for nonlinear variable fractional-order differential equations driven by L & eacute;vy noise. By establishing a novel set of suitable assumptions with the help of Picard iterations, we demonstrate the existence of unique solutions. Then, we investigate the stability of the considered fractional equations by applying the generalized Gronwall inequality and the definition of several types of stabilities, including Mittag-Leffler-Ulam-Hyers and Mittag-Leffler-Ulam-Hyers-Rassias stabilities. As an application, we present three illustrative examples attached with some numerical results to support the existing results.

引用

页数：17

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