Next Article in Journal
Sobolev-Type Neutral Stochastic Differential Equations with Hilfer Fractional Derivative and Finite Delay
Previous Article in Journal
Existence of Concentrating Solutions for Critical Hartree Equations in Perforated Domains
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Fractal Fract
Volume 10
Issue 9
10.3390/fractalfract10090651
fractalfract-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Effects of Fractional Derivative on Stability and Pattern Formation in a Time-Fractional Reaction–Diffusion Model

by
Yu Zhang
1,
Jiayu Yang
2 and
Yulan Wang
2,*
1
School of Mathematics and Statistics, Jining Normal University, Ulanqab 012000, China
2
Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, China
*
Author to whom correspondence should be addressed.
Fractal Fract. 2026, 10(9), 651; https://doi.org/10.3390/fractalfract10090651 (registering DOI)
Submission received: 28 July 2026 / Revised: 4 September 2026 / Accepted: 7 September 2026 / Published: 17 September 2026
(This article belongs to the Special Issue Advances in Fractional Diffusion Models: Random Effects and Applications)
Browse Figures
Versions Notes

Abstract

This paper investigates a time-fractional reaction–diffusion system, and develops an efficient numerical method for the system. The fractional orders serve as key bifurcation parameters, capable of inducing instabilities and rich pattern structures. We analyze and and simulate the stability conditions, bifurcation behavior, and pattern formation mechanisms of the system, and explore how variations in the fractional orders modulate the underlying dynamics.
Keywords: high-order numerical scheme; reaction–diffusion model; fractal pattern formation high-order numerical scheme; reaction–diffusion model; fractal pattern formation

Share and Cite

MDPI and ACS Style

Zhang, Y.; Yang, J.; Wang, Y. Effects of Fractional Derivative on Stability and Pattern Formation in a Time-Fractional Reaction–Diffusion Model. Fractal Fract. 2026, 10, 651. https://doi.org/10.3390/fractalfract10090651

AMA Style

Zhang Y, Yang J, Wang Y. Effects of Fractional Derivative on Stability and Pattern Formation in a Time-Fractional Reaction–Diffusion Model. Fractal and Fractional. 2026; 10(9):651. https://doi.org/10.3390/fractalfract10090651

Chicago/Turabian Style

Zhang, Yu, Jiayu Yang, and Yulan Wang. 2026. "Effects of Fractional Derivative on Stability and Pattern Formation in a Time-Fractional Reaction–Diffusion Model" Fractal and Fractional 10, no. 9: 651. https://doi.org/10.3390/fractalfract10090651

APA Style

Zhang, Y., Yang, J., & Wang, Y. (2026). Effects of Fractional Derivative on Stability and Pattern Formation in a Time-Fractional Reaction–Diffusion Model. Fractal and Fractional, 10(9), 651. https://doi.org/10.3390/fractalfract10090651

Article Metrics

Back to TopTop