EPJ ST Collection: Fractional Calculus and Time-Delayed Dynamics

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Published on 02 March 2026

Guest Editors: Mattia Coccolo, Miguel A. F. Sanjuán

The study of dynamical systems with memory has advanced rapidly in recent years, largely through two major frameworks: fractional calculus and time-delayed dynamics. Each has developed into a mature discipline with its own theories, methods, and applications, yet they have often evolved in parallel rather than in dialogue.

Fractional derivatives provide a natural framework for hereditary effects and anomalous transport through continuous memory kernels, while time delays capture explicit dependencies on past states arising from finite signal propagation or feedback. Despite their different mathematical formulations, both approaches aim to describe how the past influences the present. Striking parallels have begun to emerge: fractional operators can sometimes be interpreted as infinite-dimensional delay distributions, while time-delayed systems can reproduce long-memory effects in discrete form. This suggests a deeper, underexplored connection between the two perspectives.

A dedicated topical collection in EPJ ST is timely for several reasons:

• Bridging communities: Researchers in fractional dynamics and delayed systems rarely intersect, despite addressing similar questions.
• Clarifying parallels and differences: A comparative platform will help identify when fractional or delay modelling is most suitable, and under what conditions they yield equivalent or complementary results.
• Expanding applications: Both frameworks are increasingly used in physics, engineering, control theory, biology, and economics. A joint perspective can accelerate advances in modelling real-world systems where memory plays a key role.
• Future directions: Exploring their interplay opens new avenues for mathematical tools, hybrid models, and cross-disciplinary applications.

By consolidating these efforts, this topical collection will foster a unified understanding of memory in dynamical systems and lay the groundwork for further theoretical and applied breakthroughs.

This topical collection invites contributions that consolidate theoretical, computational, and applied research on fractional and delayed dynamics, with particular emphasis on their parallels, contrasts, and synergies. Submissions highlighting cross-fertilization between the two frameworks are especially encouraged. Potential topics include, but are not limited to:

• Conceptual parallels between fractional operators and delay terms as memory mechanisms.
• Comparative studies of stability, bifurcations, and attractor structures.
• Synchronization and control strategies: fractional vs. delayed approaches.
• Numerical and computational methods adapted to each framework.
• Applications in physics, engineering, biology, and economics.
• Cross-fertilization: insights from one framework informing the other.
• Systems combining fractional and delayed elements when useful for comparison.

We welcome two types of contributions:
Original Papers: Research articles (theoretical, experimental, or computational) presenting significant original results.
Reviews: Comprehensive reviews offering perspectives on fractional and/or delayed dynamics. Short communications or mini-reviews on recent advances are also welcome.

The outcomes of this topical collection are expected to clarify the relationships between fractional and delay-based models, foster dialogue between two vibrant research communities, and inspire new directions in theory, computation, and applications.

This topical collection will be open for submissions from 1 June 2026 and accepted contributions will be published in 2027.

Detailed author information can be found in the Submission Guidelines. For the preparation of the manuscripts a special latex template (preferably single-column layout) is available here.

EPJ ST will become a fully open access journal as of 2027.

Contributors can check their open access funding eligibility, prior to submissions, here.

Up to date Open Access agreements can be found here.

Special programs for low-income economies can found here.

Guest Editors:

Dr. Mattia Coccolo, Universidad Rey Juan Carlos, Madrid, Spain, Email: This email address is being protected from spambots. You need JavaScript enabled to view it.

Prof. Miguel A. F. Sanjuán , Universidad Rey Juan Carlos, Madrid, Spain, Email: This email address is being protected from spambots. You need JavaScript enabled to view it.