Session#1: 

Computational and Mathematical Models in Biology

Dumitru Baleanu, Carla M.A. Pinto, Juan Carlos Cortés

Computational and mathematical models are growingly being applied to study and interpret biological phenomena. New mathematical frameworks have emerged, requiring complex mathematical structures, which in turn promoted the expansion of more sophisticated computational models to provide corresponding numerical solutions. The theoretical and computational models are allied with a strong experimental approach for a quantitative validation of the results.

In this session, we kindly ask authors to submit their most valuable and updated research on computational and mathematical models in biological systems.

Topics include (but are not limited to):

• single species and population dynamics;
• modeling infectious and dynamic diseases;
• regulation of cell function;
• biological oscillators;
• biological pattern formation;
• biological networks;
• kinetic models;
• hybrid biological models;
• tumor growth and angiogenesis;
• complex biological systems;
• biomedical data;
• game theory;
• multi-agent systems;
• Monte Carlo methods;
• control theory, optimization and their applications;
• biological system with uncertainties
• inverse methods for parameters estimation in biological models;
• multiscale biological models;

Session #2

Fractional Difference Equations

Guo-Cheng Wu, Jia-Li Wei, Cheng Luo

The fractional derivatives hold memory effects. It is challenging to provide an exact discretization tool for both theoretical analysis and applications. The time scale theory can investigate dynamical systems in both continuous and discrete-time cases. This feature is particularly suitable for fractional modelings with computer implementations. In nowadays, many fractional discrete-time dynamics were successfully used in image processing, time series and big data.

This session focuses on but are not limited to:

• New discrete fractional calculus;
• Stability of fractional difference equations and applications;
• Fractional discrete-time neural networks and dynamical analysis;
• Data-driven fractional difference equations;
• New exact discretization methods of fractional operators.

Session #3

General Fractional Calculus

Guo-Cheng Wu, Babak Shiri, Qin Fan

The general fractional calculus has been paid much attention in theory and applications recently. It can be not only reduced to some well known derivatives but also reveal new ones. This new feature provides more freedom degrees in real world applications. Particularly, the general memory kernel functions can be data–dependent. However, there are some interesting problems. For example, what are general constraint conditions? What is the physical meaning of general kernel functions? As a result, this session mainly focuses on the following topics:

• Unified numerical method of fractional differential equations with general kernel functions;

• Physical meaning of the general fractional calculus;

•  Terminal value problems;

•  Neural network methods;

•  Fractional uncertain differential equations.

Session #4

ADVANCED PROCESSES OF FRACTIONAL CALCULUS AND ARTIFICIAL INTELLIGENCE IN COMPLEX SYSTEMS

Dumitru Baleanu, Yeliz Karaca

Dynamical processes and dynamical systems of fractional order in relation to natural and artificial phenomena can be modeled by ordinary or partial differential equations with integer order, which can be described aptly by employing ordinary and partial differential equations. To put differently, fractional calculus and fractional-order calculus approach enables novel models with fractional-order calculus to be employed in machine learning algorithms so that it could be possible to achieve optimized solutions caring for the need to develop analytical and numerical methods. Thereafter, while the employment of artificial intelligence allows the maximization of model accuracy and the minimization of functions like computational burden, mathematical-informed frameworks can enable reliable and robust understanding of various complex processes that involve a variety of heterogeneous temporal and spatial scales. This complexity requires a holistic understanding of different processes through multi-stage integrative models that are capable of capturing the significant attributes and peculiarities on the respective scales to expound complex systems whose behavior is confounding to predict and control with the ultimate goal of achieving a global understanding, while at the same time keeping abreast with actuality along the evolutionary and historical path, which itself, has also been through different critical points on the manifold.
Hence, importance of generating applicable solutions to problems for various engineering areas, medicine, biology, mathematical science, applied disciplines and data science, among many others, requires predictability, interpretability and reliance on mathematical sciences, with Artificial Intelligence (AI) and machine learning being at the pedestal and intersection with different fields characterized by complex, chaotic, nonlinear, dynamic and transient components to validate the significance of optimized approaches.

Based on this sophisticated integrative and multiscale approach with computer-assisted translations and applications, our special session aims at providing a bridge to merge interdisciplinary perspective to open up new pathways and crossroads both in real systems and in other related realms.

The potential topics include but are not limited to:

• Differentiability of solutions of fractional differential equations with relation to initial complex data
• Fractional stochastic differential equations
• Fractional order differential, integral equations and systems
• Computational methods for dynamical systems of fractional order
• Data-driven fractional biological modeling
• Data mining with fractional calculus methods
• Fractional order observer design for nonlinear systems
• Nonlinear modeling for biological/epidemic//neurological diseases
• Fractional differential equations with uncertainty
• Fractional dynamic processes in medicine
• Wavelet analysis and synthesis of fractional dynamics
• Entropy of complex fractional dynamics, processes and systems
• Computational medicine and/or fractional calculus in nonlinear systems
• Convolutional neural networks with fractional order gradient method
• Fractional calculus with deep neural networks
• Control and dynamics of multi-agent network systems
• Fractional calculus and computational complexity
• Nonlinear integral equations within fractional calculus in nonlinear science
• Deterministic and stochastic fractional differential equations
• Synchronization of fractional dynamic systems on time scales
• Fractional calculus with uncertainties and modeling
• Fractional-calculus-based control scheme for dynamical systems with uncertainty
• Computational intelligence-based methodologies and/or fractional techniques
• Fractional mathematical modeling with computational complexity

Among many other related points with mathematical modelling

Session#5: 

System Identification, Stability and Applications in Automatic Control

Stéphane Victor, Rachid Malti

Fractional (or non-integer) differentiation has played a very important role in various fields notably in signal and image processing and control theory. In these last fields, important considerations such as modeling, system identification, stability properties are now linked to long-range dependence phenomena. It is expected that such an invited session will attract new researchers regarding the growing research and developments on fractional calculus in the areas of mathematics, physics, engineering and particularly in automatic control. 

This invited session is devoted to research topics in the field of fractional calculus in order to present and to discuss the latest results in fractional dynamical systems and signals domain: 

• Signal analysis and filtering with fractional tools (restoration, reconstruction, analysis of fractal noises)
• System identification (linear, nonlinear, multivariable methods, etc.)
• Identifiability and Experiment design, Validation, etc. 
• Parameter estimation and Optimization 
• System stability 
• Applications (mechatronics, automotive, medical/biological systems,…)
• Fractional modeling especially of (but not limited to) thermal systems, electrical systems (motors, transformers, skin effect, etc.), dielectric materials, electrochemical systems (batteries, ultracapacitors, fuel cells, etc.), mechanical systems (vibration insulation, viscoelastic materials, etc.), biological systems (muscles, lungs, etc.)

Memorial Session

The persistence of memory for the Fractional Calculus Man JAT Machado

Virginia Kiryakova, Francesco Mainardi, Carla Pinto, Shaher Momani, Reyad El-Khazali

This memorial session will be dedicated to the memory of Prof. Jose Antonio Tenreiro Machado. His sudden demise on 6 October 2021, at age of 64, caused a shock and great lost for our Fractional Calculus collegia. We lost the never tired and ever fighting Don Quixote of the Fractional Calculus, its great promoter and so active researcher.

Till his last breath he was initiating and preparing papers, books, events and special issues, served to many journals, chaired a conference session, full of energy and life! Here are only few of words of all said then by our colleagues: “great men", “devasting sad news", “enthusiastic professional", “artist of FC", “one of pioneers of FC who helped to animate and gather our community", etc., …

Among all his colorful posters, hundreds works and attractive presentations with results and applications of FC to so wide range of areas in natural and social sciences, our community inherited recently, under his initiative and editorship, the 8 volumes of “Handbook of Fractional Calculus with Applications” (De Gruyter, 2019).

Prof. Machado was active participant and member of Steering, Program and Awarding committees for the International Conferences on Fractional Differentiation and Applications (ICFDA) since its 1^st one in Bordeaux 2004, and organizer and host of the 2^nd one in Porto 2006.

Now, at 2023 ICFDA, the traditional FDA Dissemination Award is named after JAT Machado, to honor his memory and contributions and wide range activities in popularization of FC and its applications. As a rule this award is given to individuals who have been recently most active in dissemination of Fractional Calculus among the scientific community, industry and society.

During this memorial session we plan presentations by the co-organizers, and a collection of some Machado’s posters and slides presentations on FC applications.