Deadline Date: 28 February 2027
Fractional differential equations (FDEs) have emerged as powerful mathematical tools for modeling complex phenomena characterized by memory, hereditary effects, and nonlocal behavior. Their applications have expanded rapidly across science and engineering, including viscoelasticity, anomalous diffusion, heat and mass transfer, fluid dynamics, control systems, finance, biology, signal processing, and complex network analysis. As these mathematical models become increasingly sophisticated, the development of robust, accurate, and computationally efficient numerical methods has become essential for obtaining reliable solutions and supporting scientific and engineering innovation.
Recent advances in numerical analysis, scientific computing, artificial intelligence, machine learning, and high-performance computing have significantly broadened the computational capabilities available for solving fractional-order models. New fractional operators with singular and non-singular kernels, variable-order formulations, distributed-order models, and multi-term fractional equations have introduced additional mathematical challenges that require innovative computational strategies. Consequently, there is a growing demand for efficient algorithms capable of handling nonlinearities, multi-dimensional problems, coupled systems, inverse problems, and large-scale simulations.
This Special Issue aims to provide an international platform for researchers to present recent theoretical and computational advances in the numerical treatment of fractional differential equations. The issue welcomes contributions that propose novel numerical methods, improve existing computational algorithms, provide rigorous convergence and stability analyses, or demonstrate the effectiveness of computational approaches through realistic engineering and scientific applications. Interdisciplinary studies that combine computational mathematics with modern data-driven techniques are also strongly encouraged.
The Special Issue particularly welcomes, but is not limited to, contributions in the following areas:
Numerical methods for ordinary, partial, stochastic, delay, integro-differential, and coupled fractional differential equations.
Computational methods for variable-order, distributed-order, multi-term, and nonlinear fractional models.
Development and analysis of finite difference, finite element, finite volume, spectral, meshless, wavelet, collocation, and boundary element methods.
Semi-analytical and hybrid techniques, including Adomian decomposition, homotopy methods, variational iteration methods, operational matrix approaches, transform methods, and intelligent computational algorithms.
Stability, convergence, consistency, error estimation, and adaptive numerical algorithms.
Fast iterative solvers, sparse matrix techniques, parallel computing, GPU-based algorithms, and high-performance scientific computing for fractional models.
Machine learning, physics-informed neural networks (PINNs), deep learning, surrogate modeling, and artificial intelligence-assisted computational methods for fractional differential equations.
Numerical treatment of inverse problems, parameter identification, uncertainty quantification, and data assimilation in fractional systems.
Fractional optimal control, optimization algorithms, and computational techniques for control systems.
Computational modeling of anomalous diffusion, heat transfer, wave propagation, viscoelasticity, porous media, fluid mechanics, electromagnetics, and transport phenomena.
Fractional models in biomedical engineering, epidemiology, ecology, neuroscience, finance, energy systems, materials science, and other interdisciplinary applications.
Benchmark problems, comparative numerical studies, reproducible computational frameworks, and open-source implementations for fractional differential equations.
The objective of this Special Issue is to publish high-quality original research articles and comprehensive review papers that advance computational methodologies for fractional differential equations while promoting collaboration between mathematicians, engineers, computer scientists, and researchers from applied disciplines. By bringing together contributions spanning mathematical theory, algorithm development, computational implementation, and practical applications, this Special Issue seeks to highlight emerging trends and foster future research directions in computational fractional calculus.
Editorial board
