Numerical simulation of a fractional stochastic delay differential equations using spectral scheme: a comprehensive stability analysis

The fractional stochastic delay differential equation (FSDDE) is a powerful mathematical tool for modeling complex systems that exhibit both fractional order dynamics and stochasticity with time delays. The purpose of this study is to explore the stability analysis of a system of FSDDEs. Our study e...

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Bibliographic Details
Published in:Scientific reports 2024-03, Vol.14 (1), p.6930-6930, Article 6930
Main Authors: Li, Shuo, Khan, Sami Ullah, Riaz, Muhammad Bilal, AlQahtani, Salman A., Alamri, Atif M.
Format: Article
Language:English
Subjects:
639/705/1041
639/705/1042
Biology
Calculus
Differential equations
Engineering
Fractional stochastic delay differential equations
Humanities and Social Sciences
Information science
Legendre–Gauss–Lobatto nodes
Mathematical models
Mathematics
multidisciplinary
Partial differential equations
Science
Science (multidisciplinary)
Spectral method
Stability analysis
Stochastic models
Stochasticity
Timing
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Summary:The fractional stochastic delay differential equation (FSDDE) is a powerful mathematical tool for modeling complex systems that exhibit both fractional order dynamics and stochasticity with time delays. The purpose of this study is to explore the stability analysis of a system of FSDDEs. Our study emphasizes the interaction between fractional calculus, stochasticity, and time delays in understanding the stability of such systems. Analyzing the moments of the system’s solutions, we investigate stochasticity’s influence on FSDDS. The article provides practical insight into solving FSDDS efficiently using various numerical techniques. Additionally, this research focuses both on asymptotic as well as Lyapunov stability of FSDDS. The local stability conditions are clearly presented and also the effects of a fractional orders with delay on the stability properties are examine. Through a comprehensive test of a stability criteria, practical examples and numerical simulations we demonstrate the complexity and challenges concern with the analyzing FSDDEs.
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-024-56944-z