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System theory --- Dynamics. --- System theory. --- Mathematical models. --- Systems, Theory of --- Systems science --- Science --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Philosophy

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Complex systems with symmetry arise in many fields, at various length scales, including financial markets, social, transportation, telecommunication and power grid networks, world and country economies, ecosystems, molecular dynamics, immunology, living organisms, computational systems, and celestial and continuum mechanics. The emergence of new orders and structures in complex systems means symmetry breaking and transitions from unstable to stable states. Modeling complexity has attracted many researchers from different areas, dealing both with theoretical concepts and practical applications. This Special Issue fills the gap between the theory of symmetry-based dynamics and its application to model and analyze complex systems.

History of engineering & technology --- multi-agent system (MAS) --- reinforcement learning (RL) --- mobile robots --- function approximation --- Opportunistic complex social network --- cooperative --- neighbor node --- probability model --- social relationship --- adapted PageRank algorithm --- PageRank vector --- networks centrality --- multiplex networks --- biplex networks --- divided difference --- radius of convergence --- Kung–Traub method --- local convergence --- Lipschitz constant --- Banach space --- fractional calculus --- Caputo derivative --- generalized Fourier law --- Laplace transform --- Fourier transform --- Mittag–Leffler function --- non-Fourier heat conduction --- Mei symmetry --- conserved quantity --- adiabatic invariant --- quasi-fractional dynamical system --- non-standard Lagrangians --- complex systems --- symmetry-breaking --- bifurcation theory --- complex networks --- nonlinear dynamical systems

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Complex systems with symmetry arise in many fields, at various length scales, including financial markets, social, transportation, telecommunication and power grid networks, world and country economies, ecosystems, molecular dynamics, immunology, living organisms, computational systems, and celestial and continuum mechanics. The emergence of new orders and structures in complex systems means symmetry breaking and transitions from unstable to stable states. Modeling complexity has attracted many researchers from different areas, dealing both with theoretical concepts and practical applications. This Special Issue fills the gap between the theory of symmetry-based dynamics and its application to model and analyze complex systems.

History of engineering & technology --- multi-agent system (MAS) --- reinforcement learning (RL) --- mobile robots --- function approximation --- Opportunistic complex social network --- cooperative --- neighbor node --- probability model --- social relationship --- adapted PageRank algorithm --- PageRank vector --- networks centrality --- multiplex networks --- biplex networks --- divided difference --- radius of convergence --- Kung–Traub method --- local convergence --- Lipschitz constant --- Banach space --- fractional calculus --- Caputo derivative --- generalized Fourier law --- Laplace transform --- Fourier transform --- Mittag–Leffler function --- non-Fourier heat conduction --- Mei symmetry --- conserved quantity --- adiabatic invariant --- quasi-fractional dynamical system --- non-standard Lagrangians --- complex systems --- symmetry-breaking --- bifurcation theory --- complex networks --- nonlinear dynamical systems --- multi-agent system (MAS) --- reinforcement learning (RL) --- mobile robots --- function approximation --- Opportunistic complex social network --- cooperative --- neighbor node --- probability model --- social relationship --- adapted PageRank algorithm --- PageRank vector --- networks centrality --- multiplex networks --- biplex networks --- divided difference --- radius of convergence --- Kung–Traub method --- local convergence --- Lipschitz constant --- Banach space --- fractional calculus --- Caputo derivative --- generalized Fourier law --- Laplace transform --- Fourier transform --- Mittag–Leffler function --- non-Fourier heat conduction --- Mei symmetry --- conserved quantity --- adiabatic invariant --- quasi-fractional dynamical system --- non-standard Lagrangians --- complex systems --- symmetry-breaking --- bifurcation theory --- complex networks --- nonlinear dynamical systems

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In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

Fractional calculus. --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- Derivatives and integrals, Fractional --- Differentiation of arbitrary order, Integration and --- Differintegration, Generalized --- Fractional derivatives and integrals --- Generalized calculus --- Generalized differintegration --- Integrals, Fractional derivatives and --- Integration and differentiation of arbitrary order --- Calculus --- Engineering mathematics. --- Computer simulation. --- System theory. --- Mechanical engineering. --- Computer engineering. --- Mathematical and Computational Engineering. --- Simulation and Modeling. --- Systems Theory, Control. --- Theoretical, Mathematical and Computational Physics. --- Mechanical Engineering. --- Electrical Engineering. --- Systems, Theory of --- Systems science --- Science --- Computers --- Engineering, Mechanical --- Engineering --- Machinery --- Steam engineering --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Engineering analysis --- Philosophy --- Design and construction --- Mathematics --- Systems theory. --- Applied mathematics. --- Mathematical physics. --- Electrical engineering. --- Electric engineering --- Physical mathematics --- Physics