Computational and Analytical Approaches in Fractional Calculus for Big Data and Digital Twins

Dear Colleagues,

We are pleased to invite you to submit your research for consideration to the Special Issue "Computational and Analytical Approaches in Fractional Calculus for Big Data and Digital Twins" Fractional calculus, which extends differentiation and integration to non-integer orders, has emerged as a powerful mathematical tool for modeling complex systems with memory, non-locality, and anomalous dynamics. Its integration into digital twin technology—a rapidly growing paradigm for the real-time simulation, monitoring, and optimization of physical systems—offers unprecedented accuracy and predictive capabilities. When combined with big data analytics, this synergy unlocks new capabilities for predictive modelling, decision-making, and intelligent automation.

Big data, characterized by its volume and variety, plays a critical role in digital twin environments. The non-local and memory-preserving properties of fractional calculus align naturally with the temporal and structural complexity present in large-scale data, enabling the creation of more accurate and interpretable models.

The fusion of fractional calculus with computational methods, machine learning, big data, and data-driven modeling enhances the fidelity of digital twins by incorporating long-term dependencies and more accurate system dynamics. Advances in numerical techniques for solving fractional differential equations (FDEs) and data-driven approaches have further accelerated the adoption of fractional-order models in cyber-physical systems, smart manufacturing, and complex networked systems.

This Special Issue aims to bring together original research, novel methodologies, and interdisciplinary perspectives on the application of fractional calculus in big data analytics and digital twin systems. We encourage contributions that explore both theoretical advancements and practical implementations.

The topics covered in this Special Issue include, but are not limited to, the following:

• The development and analysis of numerical methods for fractional differential equations;
• Theoretical foundations and interpretations of fractional operators in big data contexts;
• Geometrical, statistical, numerical, and physical interpretations of fractional derivatives and integrals;
• Numerical and analytical methods for solving fractional differential equations in digital twin applications;
• Computational techniques for fractional-order systems with real-time simulation and control;
• Machine learning and artificial intelligence-driven approaches for fractional calculus-based digital twins;
• Optimization and uncertainty quantification in fractional-order digital twin models;
• Applications in engineering, science, biomedicine, energy systems, and smart infrastructure;
• The multiscale modeling of cyber-physical systems with fractional dynamics;
• Fractional calculus in predictive maintenance and anomaly detection for digital twin systems;
• Hybrid methods combining fractional calculus with deep learning, neural networks, and optimization techniques.

Dr. Maria Fernanda Pires da Costa
Dr. Cecília Coelho
Dr. Luís Lima Ferrás
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• fractional calculus
• fractional differential equations
• computational modeling
• numerical methods
• machine learning
• big data
• digital twins
• engineering
• physics