Special Issue: Recent Advances in Fractal-Fractional Models with Modern Applications

2025-05-12

The special issue showcases the latest theoretical developments, computational techniques, and practical applications of fractional calculus. Fractal-fractional models, which combine the non-local, memory-retaining features of fractional derivatives with the complex geometrical structures of fractals, offer a powerful framework for describing a wide array of anomalous phenomena in nature and technology. Fractal-fractional operators combine these two perspectives by introducing differentiation and integration on fractal spaces or with fractal kernels, capturing both memory effects and spatial complexity. These models are particularly suitable for anomalous diffusion, chaotic dynamics, biological transport, and electromagnetic systems, among others. However, their analytical complexity has led to an increasing reliance on modern computational tools to analyze, solve, and interpret these models effectively.

As real-world systems often exhibit irregular, scale-dependent, and history-sensitive dynamics, the hybridization of fractal and fractional approaches has garnered significant interest across disciplines. This special issue aims to bring together contributions from applied mathematics, physics, engineering, biology, and computational sciences that explore the growing potential of these models. In addition, emphasis is placed on the integration of modern computational tools, including artificial intelligence, machine learning, and numerical optimization, to solve and analyze fractal-fractional differential equations efficiently.

Topics of Interest include (but are not limited to):

New definitions and theoretical results in fractal-fractional calculus
Analytical and numerical solutions of fractal-fractional differential equations
Fractal-fractional modeling of complex systems in physics, biology, engineering, and finance
Stability and control in systems governed by fractal-fractional dynamics
Machine learning and AI techniques applied to fractal-fractional models
Multiscale and memory-driven phenomena modeled via fractal-fractional operators
Applications in viscoelasticity, porous media, anomalous diffusion, and signal processing
Comparative analysis between classical, fractional, and fractal-fractional approaches

Lead Guest Editor:

Name: Dr. Muhammad Nadeem

Affiliation: School of Mathematics and Statistics, Qujing Normal University, China

Email: nadeem@mail.qjnu.edu.cn

Co-Guest Editor

Name: Prof. Omar Abu Arqub

Affiliation: Faculty of Science, Al-Balqa Applied University, Jordan

Email: o.abuarqub@bau.edu.jo

Important Dates

Submission Open: June 1, 2025
Submission deadline: December 31, 2025
Decision date: March 31, 2026

Submission Information

Submit it online: http://ojs.wiserpub.com/index.php/CM/user/register

Or send it to the email address: editorial-cm@wiserpub.com

Submission Guideline

https://ojs.wiserpub.com/index.php/CM/about/submissions

For any inquiries about this Special Issue, please contact the Editors via editorial-cm@wiserpub.com