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Fractal Fract
Volume 10
Issue 7
10.3390/fractalfract10070466
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Article

Limit Behavior of the Solution of Fractional Markovian Jump System Driven by Multiplicative Fractional Brownian Motion

by
Jiankang Liu
1,*,
Jiaqi Yang
1,
Wei Wei
2,
Chen Jin
1,
Kai Fan
1 and
Wei Xu
3
1
School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China
2
School of Science, Xi’an University of Architecture and Technology, Xi’an 710311, China
3
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
*
Author to whom correspondence should be addressed.
Fractal Fract. 2026, 10(7), 466; https://doi.org/10.3390/fractalfract10070466
Submission received: 28 March 2026 / Revised: 26 June 2026 / Accepted: 2 July 2026 / Published: 10 July 2026
Versions Notes

Abstract

This work is devoted to the analysis of the limit behavior of the solution to a class of fractional stochastic differential equations with Markovian switching and multiplicative fractional Brownian motion. With the aid of fractional calculus, generalized Riemann-Stieltjes integrals, stopping time techniques and inequality techniques, an averaging principle is established within the framework of Hölder continuous spaces. We prove that the solution of the original fractional Markovian jump system converges in the mean-square sense to that of the averaged equation, thereby justifying the averaging method as an effective technique for reducing the system’s complexity. Finally, concrete examples are presented to demonstrate our theoretical findings.
Keywords: averaging principle; fractional stochastic differential equations; Markovian switching; multiplicative fractional Brownian motion averaging principle; fractional stochastic differential equations; Markovian switching; multiplicative fractional Brownian motion

Share and Cite

MDPI and ACS Style

Liu, J.; Yang, J.; Wei, W.; Jin, C.; Fan, K.; Xu, W. Limit Behavior of the Solution of Fractional Markovian Jump System Driven by Multiplicative Fractional Brownian Motion. Fractal Fract. 2026, 10, 466. https://doi.org/10.3390/fractalfract10070466

AMA Style

Liu J, Yang J, Wei W, Jin C, Fan K, Xu W. Limit Behavior of the Solution of Fractional Markovian Jump System Driven by Multiplicative Fractional Brownian Motion. Fractal and Fractional. 2026; 10(7):466. https://doi.org/10.3390/fractalfract10070466

Chicago/Turabian Style

Liu, Jiankang, Jiaqi Yang, Wei Wei, Chen Jin, Kai Fan, and Wei Xu. 2026. "Limit Behavior of the Solution of Fractional Markovian Jump System Driven by Multiplicative Fractional Brownian Motion" Fractal and Fractional 10, no. 7: 466. https://doi.org/10.3390/fractalfract10070466

APA Style

Liu, J., Yang, J., Wei, W., Jin, C., Fan, K., & Xu, W. (2026). Limit Behavior of the Solution of Fractional Markovian Jump System Driven by Multiplicative Fractional Brownian Motion. Fractal and Fractional, 10(7), 466. https://doi.org/10.3390/fractalfract10070466

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