Fractional calculus (FC) has its origins dating back to the 17^th century marked by the developments of Leibniz and L'Hôpital after whom Euler made a formal definition regarding the result for a power function in the 18^th century. Early 19^th century is known for the formalization of FC along with the proposed integral definitions for the fractional derivative using integral transforms, whereas mid-19^th century led the way for the definition for a fractional operation. Last but not least, late 20^th century encountered the modern applications of FC through its modified definition by Caputo, yielding applications in engineering and physics besides being driven by applications in areas like viscoelasticity, control theory and modeling non-local phenomena as a result of the monograph authored by Oldham and Spanier (1974).

The current fundamental significance of FC rests on its capability related to the accurate modeling of systems that have memory and hereditary effects, and non-local interactions, classical or integer-order calculus may not capture. By generalizing differentiation and integration to non-integer orders, FC  ensures well-suitability for modeling systems with power-law dynamics. While standard differential operators remain local, fractional operators defined by integrals encompass the entire history of the function, suggesting their non-locality. Given that, fractional operators are the generalized versions of classical differentiation and integration operators where the order α is a non-integer (real or complex) number. The proliferation of fractional derivative definitions (i.e. Riemann-Liouville, Caputo, Caputo-Fabrizio, Atangana-Baleanu, and so forth) has posed the challenge concerning their unification and determining which of the fractional operators are more physically significant for the specific phenomena at stake. Other challenges arise from the solving of the fractional differential equations on the basis of computational-intensiveness with regard to numerical methods and analysis toward developing efficient and robust models.

Besides these, multiple nonlinear systems demonstrate phenomena where fluctuations are inclined to enhance synchronization and periodic behaviors of the system. What is more complicated is that chaos synchronization in systems has differing states, with chaotic systems being characterized by sensitivity to initial conditions marked by their inherent complexity that displays the relevance to theoretical research and practical applications. Moreover, chaotic oscillators are utilized for secure communication systems, and chaos-based optimizations can be utilized to address complex problems in different domains such as cryptography, machine learning, artificial intelligence (AI), deep learning, areas of image / signal processing, and so on. In these regards, the fractional order provides an extra degree of freedom for control design, which leads to more robust or more conveniently implemented control schemes. Furthermore, FC, in epidemiology-related settings, provides a comprehensive model to investigate real-world problems through explaining the history of infection and recovery rates. FC and Artificial Intelligence (AI) (i.e. machine learning, deep learning, convolutional neural networks, artificial neural networks) can capture the history of dynamical effects existent in different natural and artificial phenomena by their provision of an explicit physical interpretation, efficiency for practical applications and more manageable computational processes.

The convergence of advances in high-speed and applicable computing technologies along with fractional calculus has rendered computational processing analyses as a method of reasoning and the main pillar of the majority of current research, which can be of aid in tackling nonlinear dynamic challenges through novel strategies based on observations and complex data. Fractional derivatives and fractional differential equations are used extensively in modeling diverse, dynamic processes in the physical and natural world, which provides facilitation for the description of dynamic and nonlinear behaviors of nature. All these aspects are critical in the optimal prediction solutions, critical decision-making processes, optimization, quantification, automation, computer vision, multiplicity, controllability, observability, synchronization and stabilization of fractional, neural, dynamical and computational systems amongst many others. FC, thus, describes systems in various fields ranging from science and engineering to mathematics, physics, through control systems, robotics, mechanics, medicine, biology, biomedicine, bio-mathematics, epidemiology, image / signal processing, social sciences, among others.

In view of these aspects and challenges, the panel chair and panel speakers are going to engage in presentations, exchange of ideas and thought-provoking discussions. In addition to these, we are going to address selected questions, out of a pool of collected question items, concerning FC, fractional models, mathematical modeling and its applications, distinctively and / or converged, to capture the complex, real-world dynamics in different domains to ultimately hold our interactive panel.