Advanced Analysis of Discrete Fractional Operators with Computational and Neural Networking Approaches
A special issue of Mathematical and Computational Applications (ISSN 2297-8747).
Deadline for manuscript submissions: closed (15 March 2026) | Viewed by 415
Special Issue Editors
Interests: fractional calculus; fixed point theory; biostatistics; algorithms; artificial intelligence
Interests: discrete fractional calculus; fractional differential equations; computational mathematics; neural networks; machine learning in applied mathematics; fuzzy logic and fuzzy systems; mathematical modelling; numerical analysis; optimization techniques; applied computational methods
Interests: nonlinear optics; integrability; solitons; nonlinear partial differential equations; fractional calculus; integro-differential equations; nonlinear dynamical systems; analytical methods and qualitative analysis for differential equations; discrete solitons; numerical simulations; chaotic solitons; soliton stability; soliton interactions and perturbations; nonlocal solitons
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Special Issue Information
Dear Colleagues,
Discrete fractional calculus has emerged as a powerful mathematical tool for modeling memory, inheritance, and complex dynamical processes that cannot be accurately captured by traditional integer-order models. The incorporation of fractional operators in discrete domains has provided new insights into systems characterized by temporal correlations, non-locality, and multiscale interactions.
This Special Issue aims to highlight advances in discrete fractional operators and their growing significance in computational science, engineering, and intelligent systems. Fractional-order modeling in discrete frameworks connects theoretical mathematics and real-world applications, offering improved precision in areas such as control systems, signal processing, chaotic dynamics, and data-driven prediction. The development of computational algorithms and neural networking techniques has further enhanced the capacity to simulate, optimize, and interpret discrete fractional systems in both deterministic and stochastic environments.
This Special Issue welcomes contributions that investigate analytical, numerical, and intelligent computational techniques for discrete fractional operators. Papers that propose hybrid methodologies relating artificial neural networks (ANNs), deep learning, and soft computing with fractional discrete models are of particular interest. Such studies can pave the way for new paradigms in modeling memory-based systems, increasing accuracy, adaptability, and interpretability in dynamic processes. The scope of this Special Issue includes, but is not limited to, the following themes:
- Novel formulations and generalizations of discrete fractional operators;
- Existence, stability, and convergence analysis of discrete fractional systems;
- Fractional discrete models in physics, biology, finance, and engineering;
- Control and optimization of discrete-time fractional-order systems;
- Computational algorithms for solving discrete fractional differential and difference equations;
- Computational analysis of fluid dynamics with neural networking;
- Soliton analysis and nonlinear wave propagation;
- Image processing;
- Hybrid computational intelligence frameworks combining fractional calculus and machine learning;
- Stability and synchronization in neural network systems with discrete fractional dynamics.
Through this Special Issue, we aim to gather contributions that push the boundaries of mathematical theory and computational practice. Importance will be placed on innovation, methodological rigor, and interdisciplinary applications. Researchers from mathematics, computer science, physics, and engineering are encouraged to submit their latest findings. By connecting discrete fractional calculus with modern computational intelligence, this Special Issue aims to establish a robust platform for exploring how memory-dependent dynamics can be analyzed, predicted, and controlled using advanced mathematical and neural frameworks. The ultimate goal is to strengthen the theoretical foundation while fostering real-world applications in emerging technologies and complex system modeling.
Dr. Aziz Khan
Dr. Aliya Fahmi
Guest Editors
Dr. Usman Younas
Guest Editor Assistant
Manuscript Submission Information
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Keywords
- discrete fractional operators
- discrete fractional systems
- neural networking
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