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Numerical simulation of a fractional stochastic delay differential equations using spectral scheme: a comprehensive
Shuo Li1, Sami Ullah Khan2, Muhammad Bilal Riaz3,4
1School of Mathematics and Data Sciences, Changji University, Changji, 831100, Xinjiang, People's Republic of China.
Scientific Reports
|March 24, 2024
Summary
This study analyzes the stability of fractional stochastic delay differential equations (FSDDEs), exploring how fractional calculus, stochasticity, and delays interact. It offers methods for stability analysis and efficient numerical solutions for complex systems.
Area of Science:
- Mathematics
- Applied Mathematics
- Dynamical Systems
Background:
- Fractional stochastic delay differential equations (FSDDEs) model complex systems with fractional dynamics, randomness, and time delays.
- Understanding the stability of FSDDEs is crucial for analyzing and predicting the behavior of such intricate systems.
Purpose of the Study:
- To investigate the stability analysis of systems governed by FSDDEs.
- To explore the interplay between fractional calculus, stochasticity, and time delays in determining system stability.
- To provide practical insights into efficient numerical methods for solving FSDDEs.
Main Methods:
- Analysis of the moments of system solutions to understand stochasticity's impact.
- Focus on both asymptotic and Lyapunov stability criteria.
- Derivation and presentation of local stability conditions.
- Examination of the influence of fractional orders and delays on stability properties.
Main Results:
- Demonstration of the complexity and challenges inherent in analyzing FSDDEs.
- Validation of stability criteria through practical examples and numerical simulations.
- Clear presentation of local stability conditions and their dependence on system parameters.
Conclusions:
- The study enhances understanding of FSDDE stability by integrating fractional calculus, stochasticity, and time delays.
- Efficient numerical techniques are presented for practical problem-solving.
- The research highlights the critical role of fractional orders and delays in shaping system stability.
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