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Advanced stability analysis of a fractional delay differential system with stochastic phenomena using spectral
Mengqi Xie1, Sami Ullah Khan2, Wojciech Sumelka3
1Department of Electronic Information Engineering, Xi'an Technological University, Xi'an, 710021, China.
Scientific Reports
|May 27, 2024
Summary
This study introduces a new spectral method for analyzing the stability and numerical solutions of fractional stochastic delay systems. The approach effectively models complex systems with memory and uncertainty, validated by numerical simulations.
Area of Science:
- Dynamical Systems
- Fractional Calculus
- Stochastic Processes
Background:
- Fractional calculus is increasingly used to model systems with memory and uncertainty.
- Fractional stochastic delay differential equations are vital for complex dynamical systems.
- Existing methods may not fully capture the nuances of these systems.
Purpose of the Study:
- To develop and present a novel spectral approach for analyzing fractional stochastic delay systems.
- To investigate the stability behavior and numerical solutions of these complex systems.
- To bridge fractional calculus, stochastic processes, and spectral analysis.
Main Methods:
- A novel spectral approach is employed.
- The method focuses on stability analysis and numerical solutions.
- Theoretical findings are validated through numerical simulations.
Main Results:
- The spectral approach effectively demonstrates the stability behavior of fractional stochastic delay systems.
- Numerical solutions for these systems are accurately obtained.
- The study provides a validated analytical tool for complex dynamics.
Conclusions:
- The proposed spectral method offers a robust way to analyze fractional stochastic delay systems.
- This work enhances understanding of systems with memory, uncertainty, and time delays.
- The findings contribute to the field of fractional dynamics and analytical tools.
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