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This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems.

complexity --- cuckoo search --- magnetic resonance imaging --- fractional calculus --- musical signal --- pinning synchronization --- Fourier transform --- optimal randomness --- fractional-order system --- Mittag-Leffler function --- meaning --- parameter --- diffusion-wave equation --- anomalous diffusion --- Laplace transform --- time-varying delays --- mass absorption --- swarm-based search --- fractional --- adaptive control --- time series --- Hurst exponent --- fractional derivative --- control --- PID --- global optimization --- reaction–diffusion terms --- audio signal processing --- Caputo derivative --- harmonic impact --- fractional complex networks --- heavy-tailed distribution --- impulses --- long memory --- linear prediction

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In recent years, fractional calculus has led to tremendous progress in various areas of science and mathematics. New definitions of fractional derivatives and integrals have been uncovered, extending their classical definitions in various ways. Moreover, rigorous analysis of the functional properties of these new definitions has been an active area of research in mathematical analysis. Systems considering differential equations with fractional-order operators have been investigated thoroughly from analytical and numerical points of view, and potential applications have been proposed for use in sciences and in technology. The purpose of this Special Issue is to serve as a specialized forum for the dissemination of recent progress in the theory of fractional calculus and its potential applications.

Caputo fractional derivative --- fractional differential equations --- hybrid differential equations --- coupled hybrid Sturm–Liouville differential equation --- multi-point boundary coupled hybrid condition --- integral boundary coupled hybrid condition --- dhage type fixed point theorem --- linear fractional system --- distributed delay --- finite time stability --- impulsive differential equations --- fractional impulsive differential equations --- instantaneous impulses --- non-instantaneous impulses --- time-fractional diffusion-wave equations --- Euler wavelets --- integral equations --- numerical approximation --- coupled systems --- Riemann–Liouville fractional derivative --- Hadamard–Caputo fractional derivative --- nonlocal boundary conditions --- existence --- fixed point --- LR-p-convex interval-valued function --- Katugampola fractional integral operator --- Hermite-Hadamard type inequality --- Hermite-Hadamard-Fejér inequality --- space–fractional Fokker–Planck operator --- time–fractional wave with the time–fractional damped term --- Laplace transform --- Mittag–Leffler function --- Grünwald–Letnikov scheme --- potential and current in an electric transmission line --- random walk of a population --- fractional derivative --- gradient descent --- economic growth --- group of seven --- fractional order derivative model --- GPU --- a spiral-plate heat exchanger --- parallel model --- heat transfer --- nonlinear system --- stochastic epidemic model --- malaria infection --- stochastic generalized Euler --- nonstandard finite-difference method --- positivity --- boundedness --- n/a --- coupled hybrid Sturm-Liouville differential equation --- Riemann-Liouville fractional derivative --- Hadamard-Caputo fractional derivative --- Hermite-Hadamard-Fejér inequality --- space-fractional Fokker-Planck operator --- time-fractional wave with the time-fractional damped term --- Mittag-Leffler function --- Grünwald-Letnikov scheme

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This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.

heteroclinic solutions --- non-instantaneous impulses --- Schauder’s fixed point theory --- dichotomy --- second-order differential/difference/q-difference equation of hypergeometric type --- differential equations --- a priori estimates --- global solutions --- generalized Liouville equation --- Hilbert space --- dissipation --- collocation method --- exponential dichotomy --- Sumudu decomposition method --- three-step Taylor method --- dynamical system --- lower and upper solutions --- problems in the real line --- Nagumo condition on the real line --- SIRS epidemic model --- first order periodic systems --- regular solutions --- Clairin’s method --- coupled nonlinear systems --- Navier–Stokes equations --- Bäcklund transformation --- asymptotic stability --- Caputo fractional derivative --- exponential stability --- difference equations --- lipschitz stability --- strong nonlinearities --- polynomial solution --- integro-differentials --- kinetic energy --- Legendre wavelets --- weak solutions --- discrete Lyapunov equation --- population dynamics --- non-uniform lattices --- Korteweg-de Vries equation --- time-dependent partial differential equations --- mean curvature operator --- functional boundary conditions --- mathematical modelling --- fixed point theory --- limit-periodic solutions --- Arzèla Ascoli theorem --- Miura transformation --- state dependent delays --- ?-Laplacian operator --- divided-difference equations --- effective existence criteria

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This book is a collection of recent publications from researchers all over the globe in the broad area of high-voltage engineering. The presented research papers cover both experimental and simulation studies, with a focus on topics related to insulation monitoring using state-of-the-art sensors and advanced machine learning algorithms. Special attention was given in the Special Issue to partial discharge monitoring as one of the most important techniques in insulation condition assessment. Moreover, this Special Issue contains several articles which focus on different modeling techniques that help researchers to better evaluate the condition of insulation systems. Different power system assets are addressed in this book, including transformers, outdoor insulators, underground cables, and gas-insulated substations.

artificial neural network --- simulation --- high-frequency --- artificial flashover tests --- wide bandgap power modules --- tracking --- electrical field strength --- fast-rise square wave voltages --- FDTD simulation --- cable joint --- corona discharge --- feature selection --- post insulator --- earthing systems --- wind speed --- surface discharge --- oil/paper insulation --- oil-paper insulation --- high-magnitude currents and impulse polarity --- UFVM --- Tettex 9520 --- electrical tree --- flashover characteristics --- composite insulator --- partial discharge --- numerical modeling --- saline mechanism --- thermal parameters --- space charge density --- seasonal --- ion flow field --- denoising --- DDX 9121b --- temperature --- transformer asset management --- cavity discharge --- space/interface charge --- insulation health index --- heat transfer model --- leakage current --- machine learning --- partial discharges (PD) --- RF signal --- flashover --- high impulse conditions --- grounding electrodes --- generalized finite difference time domain --- curve fitting --- grounding --- plasma discharge --- outdoor insulators --- flashover dynamic model --- wavelet transform --- degradation --- thermal properties --- bipolar charge transport model --- UHF sensor --- cable --- random walk theory --- tracking test setup --- GIL --- pressure --- modelling --- non-uniform pollution between windward and leeward sides --- calibrator --- secondary arc --- polymeric insulation --- optical-UHF integrated detection --- shoreline --- dry band arcing --- photoelectric fusion pattern --- DDX 8003 --- XLPE --- silicone gel --- partial discharge modeling --- electric field analysis --- NSCT --- electrode’s geometry --- gas --- Comsol Multiphysics --- fast-impulses --- laying modes --- ageing --- cable ampacity --- residual resistance formulation --- finite element analysis --- thermal effect --- hydrophobicity --- soil resistivity --- charge simulation method --- short-circuit discharge --- dry band formation

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Cellular signal transduction --- Cell receptors --- Signal transduction --- Cell interaction --- Transduction du signal cellulaire --- Récepteurs cellulaires --- Cellules --- Periodicals. --- Périodiques --- Interaction --- Synaptic Transmission. --- Signal Transduction. --- Cell receptors. --- Cellular signal transduction. --- Neurophysiologie. --- Biosignal. --- Rezeptor. --- Receptors, Cell Surface --- Cell Communication --- Cell Interaction --- Cell-to-Cell Interaction --- Cell Communications --- Cell Interactions --- Cell to Cell Interaction --- Cell-to-Cell Interactions --- Communication, Cell --- Communications, Cell --- Interaction, Cell --- Interaction, Cell-to-Cell --- Interactions, Cell --- Interactions, Cell-to-Cell --- Cell Surface Hormone Receptors --- Endogenous Substances Receptors --- Cell Surface Receptors --- Hormone Receptors, Cell Surface --- Receptors, Endogenous Substances --- Binding Sites --- Hormones --- Ligands --- Receptor Cross-Talk --- Transmission, Neural --- Transmission, Synaptic --- Neural Transmission --- Neurotransmission --- Neural Conduction --- Synapses --- Receptor Mediated Signal Transduction --- Signal Transduction Pathways --- Signal Transduction Systems --- Receptor-Mediated Signal Transduction --- Signal Pathways --- Pathway, Signal --- Pathway, Signal Transduction --- Pathways, Signal --- Pathways, Signal Transduction --- Receptor-Mediated Signal Transductions --- Signal Pathway --- Signal Transduction Pathway --- Signal Transduction System --- Signal Transduction, Receptor-Mediated --- Signal Transductions --- Signal Transductions, Receptor-Mediated --- System, Signal Transduction --- Systems, Signal Transduction --- Transduction, Signal --- Transductions, Signal --- Receptor-CD3 Complex, Antigen, T-Cell --- Feedback, Physiological --- Gasotransmitters --- Periodicals --- Chemistry --- Health Sciences --- Life Sciences --- Biochemistry --- Neurology --- Physiology --- neurobiology --- pharmacology --- cell biology --- neuroendocrinology --- neurology --- Nervenphysiologie --- Nervensystem --- Cell membrane receptors --- Cell surface receptors --- Receptors, Cell --- Cellular information transduction --- Information transduction, Cellular --- Signal transduction, Cellular --- Physiologie --- Signal Transduction --- Synaptic Transmission --- Neurologie --- Hirnforschung --- Binding sites (Biochemistry) --- Cell membranes --- Proteins --- Bioenergetics --- Cellular control mechanisms --- Information theory in biology --- Cell Signaling --- Cell Surface Receptor --- Receptor, Cell Surface --- Surface Receptor, Cell --- Neurophysiologie --- Biosignal --- Rezeptor --- Neural transmission. --- Transmission nerveuse. --- Transduction du signal cellulaire. --- Nerve transmission --- Nervous transmission --- Synaptic transmission --- Transmission of nerve impulses --- Neural circuitry --- Neurophysiology --- Neurotransmitters