Deadline Date: 30 April 2026
This special issue on Numerical Methods for Nonlinear Mathematical Models with Engineering Applications is dedicated to exploring and advancing the development of computational approaches for the analysis and solution of complex mathematical models arising in engineering sciences. These models are critical for understanding various phenomena such as heat transfer, fluid dynamics, and other related areas where traditional analytical techniques often fall short due to the inherent nonlinearities and complexities involved. In particular, this issue places a strong emphasis on recent progress in the field of numerical methods for fractional differential equations (FDEs), especially those of a time-fractional nature. These equations, which extend classical integer-order differential equations, have become a powerful tool in modeling processes with memory, hereditary effects, and anomalous dynamics. Their applications are widespread and significant, encompassing disciplines such as viscoelastic material behavior, transport in porous media, anomalous diffusion, bioengineering, signal processing, and control systems.
The complexity of these models is further compounded when they include nonlinear terms, time delays, singular or nonsmooth initial conditions, and coupled systems. These features pose substantial challenges not only in theoretical analysis but also in the development of accurate and efficient numerical solvers. The nonlocal and singular nature of fractional derivatives requires innovative computational strategies to ensure both stability and accuracy over long time simulations.
This special issue aims to gather high-quality original research articles and review papers that propose novel numerical algorithms, provide rigorous error analysis, or demonstrate significant engineering applications of these methods. We also welcome contributions that incorporate machine learning techniques including physics informed neural networks, operator learning, and data driven surrogate modeling. These approaches are especially useful for accelerating simulations and approximating complex fractional dynamics where analytical solutions are unavailable. Topics of interest include, but are not limited to, finite difference and finite element methods for FDEs, spectral methods, meshless methods, and hybrid approaches tailored for nonlinear fractional systems. Contributions addressing the modeling, simulation, and real-world applications of such methods in engineering contexts are especially welcome.
Editorial board
