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Submit a Manuscript to the Journal
Applied Mathematics in Science and Engineering

For a Special Issue on
Advanced Fractals and Fractional Calculus with Science and Engineering Applications: Computing, Dynamics and Control in Complex Systems

Manuscript deadline
31 December 2022

Cover image - Applied Mathematics in Science and Engineering

Special Issue Editor(s)

Yeliz Karaca, University of Massachusetts Medical School, Worcester, USA
[email protected]

Dumitru Baleanu, Çankaya University, Ankara, Türkiye and Institute of Space Sciences, Magurele-Bucharest, Romania
[email protected]

Yu-Dong Zhang, University of Leicester, Leicester, UK
[email protected]

Praveen Agarwal, Anand International College of Engineering, India
[email protected]

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Advanced Fractals and Fractional Calculus with Science and Engineering Applications: Computing, Dynamics and Control in Complex Systems

Complex and nonlinear dynamic models are characterized by intricate attributes like high dimensionality and heterogeneity, having fractional-order derivatives and constituting fractional calculus, which brings forth a thorough comprehension, control and optimization of the related dynamics and structure. This requirement, posing a daunting challenge, has gained prominence in different fields of science where fractional derivatives and nonlinearities interact. Fractional models have, correspondingly, become relevant to deal with phenomena with memory effects in contrast with traditional models of ordinary and partial differential equations. When compared with integer-order calculus that constitutes the mathematical basis of most control systems, fractional calculus provides better equipment to deal with the time-dependent impacts observed. Analysis and control of fractional order nonlinear systems seem to be another challenge with the observation of unknown inputs and concepts being used and analytically derived. Being a noteworthy attribute of complex systems, nonlinearity represents the various interactions between the variables in a nonlinear fashion. Emergence, feedback, adaptiveness, irreducibility, chaos, operating between order and chaos, having multilayers of structure as well as self-organization are among some of the other attributes. Multiple nonlinear complex systems demonstrate phenomena where oscillations improve periodic behaviors and synchronization of the system. Therein, the aggregate of parts is in fact not equal to the sum of their characteristics, behaviors and actions.

Fractional dynamics, along with fractional calculus, through the investigation of fractional-order integral and derivative operators with real or complex domains in science and engineering, has accordingly merged with the advances in the high-speed and applicable computing technologies; and hence, computational processing analyses, as a method of reasoning and a main pillar of majority of current research, can be of aid to tackle nonlinear dynamic problems in complex systems through novel strategies based on observations and complex data. Besides this aspect, tackling uncertainty in multiple attribute group decision-making processes is required to attain exact, precise and intelligent solutions in real life, which is characterized by the complexity in engineering, scientific, social and economic environments. To this end, to be able to provide feasible and applicable solutions within the dynamic processes of the complex nonlinear systems, methods related to analytical, numerical, simulation-related and computational analyses can be employed by taking into consideration the control-theoretic aspects thereto associated. Thus, this stance can enable to bridge the gap between mathematics and computer science besides the other wide array of sciences so that transition from integer to fractional order methods can be ensured. Along this strand, fractional derivatives and fractional differential equations are extensively employed in the mathematical modeling of diverse dynamic processes in the physical and natural world, providing ample aid for the accurate description of complex, dynamic and nonlinear behaviors of nature. All these aspects are important for the optimal prediction solutions, critical decision-making processes, optimization, quantification, multiplicity, controllability, observability and stabilization of fractional, neural and computational systems amongst many others.

This sophisticated approach has become more prominent in nonlinear dynamic systems, facilitating to achieve enabling solutions, optimization processes, numerical simulations besides technical analyses and related applications in areas like mathematics, medicine, neuroscience, engineering, physics, biology, virology, chemistry, genetics, information science, computer science, information and communication technologies, informatics, space sciences, applied sciences, public health, finance, economics and social sciences to name some. Accordingly, our special issue aims to provide a way towards original multidisciplinary and intrinsic goal-oriented research based on advanced mathematical modeling and computational foundations, so we expect to get studies submitted on theoretical and applied dimensions of nonlinear, dynamic and complex systems merging mathematical analysis, methods and computing technologies to be presented in order to demonstrate the significance of novel approaches in real systems and related realms.

The potential topics of our special issue include but are not limited to:
- Computational methods for dynamical systems of fractional order
- Fractional calculus of variations and optimal control with time-scale
- Fractional calculus with computational complexity
- Data-driven forecasting of high-dimensional chaotic systems
- Data-driven fractional biological modeling
- Control/optimization of dynamical systems
- Fractional hypergeometric functions and applications in science and engineering
- Synchronization of dynamic systems on time scales
- Data mining with fractional calculus methods
- Fractional order observer design for nonlinear systems
- Adaptive tracking control for multiple unknown fractional-order systems
- Nonlinear control for epidemic/biological diseases
- Mathematical epidemiological modelling for dynamic infectious/viral diseases
- Fractional differential equations with uncertainty
- Fractional dynamic processes in medicine
- Fractional calculus with artificial intelligence applications
- Image / signal analyses based on soft computing
- Fuzzy fractional calculus
- Wavelet analysis and synthesis of fractional dynamics
- Entropy of Complex dynamics, processes and systems
- Nonlinear periodicity and synchronization
- Mathematical modelling of Complex systems
- Quantization optimization algorithms
- Integrative machine-learning and neuroscience
- Computational medicine and fractional calculus in nonlinear systems
- Control and dynamics of multi-agent network systems
- Computational complexity
- Nonlinear integral equations within fractional calculus in nonlinear science
- Signal processing and design for scalar conservation laws
- Deterministic and stochastic fractional differential equations
- Stochastic dynamics of nonlinear dynamic systems
- Fractional calculus with uncertainties and modeling
- Fractional dynamic processes in medicine
- Fractional-calculus-based control scheme for dynamical systems with uncertainty
- Control theory, optimization and their applications in Complex systems
- Computational intelligence-based methodologies and techniques
- Neural computations with fractional calculus
- Bifurcation and chaos in Complex systems
- Quantum computation and optimization models of Complex systems
- Special functions in fractional calculus context
- Optimal synergetic control for fractional-order systems
- Artificial Intelligence in Complex systems
- Cyber-human system modeling and control with fractional order dynamics

Submission Instructions

Important deadlines for submission:
Initial submission: July 1, 2022
Closing date for initial submission: December 31, 2022 (Part I)
Deadline for final decision notification: May 31, 2023
Subsequent continuing parts are being planned as Part II and more parts.

Instructions for AuthorsSubmit an Article

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