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Updated: May 28, 2026

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

Dynamic analysis of the fractional distributed delay models.

H A A El-Saka¹, D El A El-Sherbeny^2,3, A M A El-Sayed⁴

¹Mathematics Department, Faculty of Science, Damietta University, New Damietta, 34517, Egypt. halaelsaka@du.edu.eg.

Scientific Reports

|May 26, 2026

Summary

This study analyzes fractional distributed delay models by converting them into fractional order systems. We determined how fractional order and delays impact model stability, confirming findings with simulations.

Keywords:

Distributed delay models Incommensurate fractional order systems Numerical solutions Stability analysis

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Last Updated: May 28, 2026

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

Area of Science:

Dynamical Systems
Fractional Calculus
Mathematical Biology

Background:

Fractional distributed delay models are crucial for systems with memory effects.
Understanding the stability of these models is essential for predicting system behavior.
Previous research has explored various aspects of fractional models, but stability analysis in distributed delay systems requires further investigation.

Purpose of the Study:

To analyze the stability of fractional distributed delay models.
To investigate the influence of fractional order and delay parameters on model stability.
To compare the effect of distributed delay on stability regions using the fractional order delay logistic equation.

Main Methods:

Utilizing the linear chain trick to transform models into incommensurate fractional order systems.
Analyzing the characteristic equation around equilibrium points to determine stability regions.
Employing numerical simulations to validate analytical stability results.

Main Results:

The stability regions of fractional distributed delay models were successfully determined.
Key parameters such as fractional order (α), ρ, and 'a' were shown to significantly affect model stability.
The influence of distributed delay on stability was quantified and compared for the logistic equation.

Conclusions:

The stability of fractional distributed delay models can be effectively analyzed using the linear chain trick.
Fractional order and delay parameters play a critical role in shaping the stability landscape of these models.
Numerical simulations corroborate the analytical findings, providing confidence in the derived stability criteria.