Deadline Date: 31 December 2026
Fractional-order differential equations (FODEs) have emerged as a powerful tool for modeling complex systems in both engineering and biological sciences. Unlike traditional integer-order models, FODEs incorporate memory effects and non-local interactions, making them particularly suited to describe phenomena that exhibit long-term dependence or hereditary properties. As a result, they have gained increasing attention in areas such as disease dynamics, material science, and engineering systems, where traditional integer-order models fall short. However, solving these equations presents significant computational challenges due to the non-local nature of fractional derivatives and the complexity of high-dimensional systems.
This special issue aims to explore advanced computational techniques and numerical methods for solving fractional-order differential equations. We seek to highlight the latest developments in this area, focusing on both theoretical advances and real-world applications. The issue will cover the computational challenges inherent in FODEs, the role of high-performance computing, and the integration of machine learning techniques to tackle these complex models. We invite contributions from researchers working on innovative numerical schemes, parallel computing approaches, and software tools for efficiently solving FODEs across various domains. The scope of the special issue will encompass both the theoretical underpinnings of fractional calculus and its practical implementation, with an emphasis on engineering systems and disease dynamics. We aim to foster collaboration between computational mathematicians, engineers, and biologists, contributing to a more unified approach to modeling complex systems.
- We invite papers on, but not limited to, the following topics:
- Numerical methods for solving fractional-order differential equations.
- Computational challenges and solutions for FODEs, including stability and convergence analysis.
- Applications of fractional-order models in engineering systems, such as materials modeling, diffusion, and fluid dynamics.
- Use of fractional-order differential equations in disease dynamics and epidemiological modeling.
- The integration of machine learning and AI techniques with fractional-order models.
- Development and optimization of computational tools and software for solving FODEs.
- High-performance computing and parallelization techniques for large-scale simulations of fractional-order systems.
Editorial board
