Novel and Effective Applications of Fractional-Order Models

Dear Colleagues,

Mathematical modelling elucidates real-world interactions and their dynamics through precise representation. Such models aim to capture universal principles enabling mechanization, prediction, and robust decision making. Fractional calculus (FC) is a growing pillar in modelling, impacting system identification, control, materials, and biology. Fractional-order models can flexibly describe memory-rich phenomena that classical integer-order models cannot. Their applications span viscoelasticity, anomalous diffusion, electrochemical processes, biomedical dynamics, and long-range dependent systems.

In control, FC enriches dynamic via fractional operators, capturing history-dependent and local effects more accurately. Fractional-order controllers (e.g., FOPID PI^λD^μ) add two tunable orders, boosting design flexibility and robustness beyond FOPID. Fractional-state-space observers with sliding mode, adaptive, and optimal control expand FO methodologies. This Special Issue invites contributions across theory, design, validation, and real-world FC modelling applications. Areas of interest for submission encompass, but are not limited to, the following:

• Fractional-order system identification and model reduction
• Fractional-order controllers (FOPID, fractional-order PI, PD, and robust variants)
• Fractional-order state-space, observers, and estimation techniques
• Fractional-order model predictive control and optimization
• Fractional-order adaptive, robust, and sliding mode control
• Fractional-order filters, neural networks, and data-driven approaches for FO dynamics
• Fractional diffusion, viscoelastic, electrochemical, and bioengineering applications
• Fractional-order Kalman filtering and estimation in noisy or uncertain environments
• Stability analysis, robustness metrics, and isodamping/isodromic criteria for FO systems
• Numerical methods, discretization, and implementation issues for real-time FO control
• Experimental validation and real-world case studies across engineering, physics, biology, and finance
• Multi-model and switching strategies for systems with fractional dynamics
• Hybrid and composite models combining fractional and integer-order components
• Theoretical insights and design strategies of FOPID;
• Approximation of fractional-order elements in digital and analog Domains.
• Real-world Implementation of FOPID.
• Empirical validation through experimental implementations.
• Wide-ranging applications of fractional-order control strategies.

We invite contributions that shed light on these topics, showcasing cutting-edge research and practical applications in the realm of fractional-order control.

Dr. Carla M. A. Pinto
Dr. Cristina I. Muresan
Dr. Dana Copot
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 250 words) can be sent to the Editorial Office for assessment.

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-order modeling
• fractional-order control
• FOPID controllers
• fractional-order system identification
• stability and robustness analysis
• numerical implementation and approximation
• real-world applications and experimental validation