New Horizons in Fractional and Fractal Dynamics: Unraveling Complexity in Chaotic Systems

Dear Colleagues,

The study of chaotic systems has long been a cornerstone of nonlinear dynamics, revealing the intricate and often unpredictable behaviors that emerge from simple deterministic rules. In recent years, the fields of fractional calculus and fractal geometry have emerged as powerful tools for unraveling the complexities inherent in these systems.

This special issue aims to highlight pioneering research and cutting-edge developments at the dynamic intersection of fractional dynamics, fractal analysis, and chaotic systems. We seek high-quality contributions that advance theoretical understanding, introduce novel computational and analytical methodologies, and demonstrate impactful applications across a wide range of scientific and engineering disciplines. Submissions may address, but are not limited to, the following areas:

1. New fractional-order chaotic/hyperchaotic system models.
2. Stability analysis and bifurcation phenomena in fractional-fractal systems.
3. Complexity measures integrating fractional dynamics and fractal structures.
4. Novel numerical techniques for simulating high-dimensional fractional chaotic systems with fractal properties.
5. Advanced algorithms for estimating fractal dimensions and multifractal parameters from fractional chaotic time series.
6. Machine learning/AI approaches for analyzing fractional-fractal chaos.
7. Relationships between fractional operators and emergent fractal properties.
8. Dynamics and control of networks with fractional node dynamics and fractal connection topologies.
9. Modeling neural dynamics, cardiac rhythms, biological oscillators with memory and fractal scaling.
10. Fractional-fractal models for market volatility, asset pricing, and economic time series analysis.
11. Fault diagnosis, signal processing, power systems stability, memristor-based chaotic circuits with fractional elements.
12. Utilizing the high complexity of fractional-fractal chaos for robust security.

Prof. Dr. Song Zheng
Dr. Liguo Yuan
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• fractional-order systems
• stability analysis
• fractional-order control theory
• high-dimensional fractional-fractal simulation
• chaotic time series analysis
• machine learning for fractional chaos
• fractal network dynamics
• biological oscillator modeling
• economic fractal models
• security encryption applications