Nonlinear dynamic models are characterized by marked attributes like high dimensionality and heterogeneity, having fractional-order derivatives, and constituting fractional calculus, which brings forth a thorough comprehension and control of the related dynamics, constituents and structure. Fractional dynamics with its interdisciplinary nature examines the nonlocal properties of dynamical systems through the methods pertaining to fractional calculus, integro-differential equations of non-integer orders as well as discrete nonlocal mappings. Regarded as a nonlocal system of any nature, a fractional dynamical system displays states of changes that could be discrete or continuous in time. Fractional-order system refers to a dynamical system whose modeling can be attained by a fractional differential equation that includes derivatives of non-integer order.

Fractional calculus, extending traditional calculus by enabling the differentiation and integration of non-integer orders, proves itself as a robust means applications, biology, mechanics and engineering, among other fields. Accordingly, fractional models have become relevant to dealing with phenomena with memory effects in contrast with traditional models of ordinary and partial differential equations. Compared with integer-order calculus, which constitutes the mathematical basis of most control systems, fractional calculus can provide better equipment to handle the observed time-dependent impacts and generalized memory.

The advances attained in science and applied mathematics have led to the discovery of physical systems described with differential fractional-order equations in which a fractional derivative order is used. Thus, such systems cannot be modeled effectively by using the classical differential integer-order equations; consequently, fractional-order systems are investigated along with various problems inside the control theory including state estimation, control-fault diagnosis, and so on. Analysis and control of fractional order nonlinear systems are also significant, along with the observation of unknown inputs and concepts being used and derived analytically. Multiple nonlinear systems demonstrate phenomena in which fluctuations enhance synchronization and periodic behaviors of the system. Chaos synchronization in systems has differing states, and chaotic systems are characterized by sensitivity to initial conditions with their inherent complexity manifesting the relevance to theoretical research and practical applications. Moreover, chaotic oscillators are utilized for secure communication systems, and chaos-based optimizations can be resorted to for addressing complex problems in different domains such as cryptography, machine learning, artificial intelligence (AI), deep learning, areas of signal processing, and so on.

The merging of advances in high-speed and applicable computing technologies along with fractional calculus, through the investigation of fractional-order integral and derivative operators with real or complex domain, has rendered computational processing analyses as a method of reasoning and the main pillar of the majority of current research. These can be of aid in tackling nonlinear dynamic problems through novel strategies based on observations and complex data. To be able to provide feasible and applicable solutions within the dynamic processes of the nonlinear systems, methods related to analytical, numerical, simulation-related, and computational analyses can be employed by considering the control-theoretic aspects to that associated. Thus, this stance enables one to provide a bridge between mathematics and computer science besides other wide range of sciences so that transition from integer to fractional order methods can be ensured. 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, multiplicity, controllability, observability, synchronization and stabilization of fractional, neural, dynamical and computational systems amongst many others.

This integrative sophisticated approach, with the theoretical and applied dimensions of nonlinear dynamic systems merging fractional mathematics and computing technologies to be presented to demonstrate the significance of novel approaches in the related realms have become more prominent in nonlinear dynamic systems, facilitating to achieve viable solutions, optimization processes, numerical simulations besides technical analyses and related applications in areas, including mathematics, medicine, engineering, physics, mechanics, biology, virology, chemistry, genetics, information science, information and communication technologies, informatics, data science, computer science, space sciences, applied sciences, finance and social sciences, to name some. Accordingly, our symposium aims at providing a productive platform to pave the way for novel research, fruitful discussions as well as thought-provoking experiences.

The potential topics of our symposium include but are not limited to: