Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The topic of this book is the mathematical and numerical analysis of some recent frameworks based on differential equations and their application in the mathematical modeling of complex systems, especially of living matter. First, the recent new mathematical frameworks based on generalized kinetic theory, fractional calculus, inverse theory, Schrödinger equation, and Cahn–Hilliard systems are presented and mathematically analyzed. Specifically, the well-posedness of the related Cauchy problems is investigated, stability analysis is also performed (including the possibility to have Hopf bifurcations), and some optimal control problems are presented. Second, this book is concerned with the derivation of specific models within the previous mentioned frameworks and for complex systems in biology, epidemics, and engineering. This book is addressed to graduate students and applied mathematics researchers involved in the mathematical modeling of complex systems.

boundedness --- delay --- Hopf bifurcation --- Lyapunov functional --- stability --- SEIQRS-V model --- kinetic theory --- integro-differential equations --- complex systems --- evolution equations --- thermostat --- nonequilibrium stationary states --- discrete Fourier transform --- discrete kinetic theory --- nonlinearity --- fractional operators --- Cahn–Hilliard systems --- well-posedness --- regularity --- optimal control --- necessary optimality conditions --- Schrödinger equation --- Davydov’s model --- partial differential equations --- exact solutions --- fractional derivative --- abstract Cauchy problem --- C0−semigroup --- inverse problem --- active particles --- autoimmune disease --- degenerate equations --- real activity variable --- Cauchy problem --- electric circuit equations --- wardoski contraction --- almost (s, q)—Jaggi-type --- b—metric-like spaces --- second-order differential equations --- dynamical systems --- compartment model --- epidemics --- basic reproduction number

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This Special Issue was intended as a forum to advance research and apply machine-learning and data-mining methods to facilitate the development of modern electric power systems, grids and devices, and smart grids and protection devices, as well as to develop tools for more accurate and efficient power system analysis. Conventional signal processing is no longer adequate to extract all the relevant information from distorted signals through filtering, estimation, and detection to facilitate decision-making and control actions. Machine learning algorithms, optimization techniques and efficient numerical algorithms, distributed signal processing, machine learning, data-mining statistical signal detection, and estimation may help to solve contemporary challenges in modern power systems. The increased use of digital information and control technology can improve the grid’s reliability, security, and efficiency; the dynamic optimization of grid operations; demand response; the incorporation of demand-side resources and integration of energy-efficient resources; distribution automation; and the integration of smart appliances and consumer devices. Signal processing offers the tools needed to convert measurement data to information, and to transform information into actionable intelligence. This Special Issue includes fifteen articles, authored by international research teams from several countries.

Technology: general issues --- History of engineering & technology --- Energy industries & utilities --- virtual power plant (VPP) --- power quality (PQ) --- global index --- distributed energy resources (DER) --- energy storage systems (ESS) --- power systems --- long-term assessment --- battery energy storage systems (BESS) --- smart grids --- conducted disturbances --- power quality --- supraharmonics --- 2-150 kHz --- Power Line Communications (PLC) --- intentional emission --- non-intentional emission --- mains signalling --- virtual power plant --- data mining --- clustering --- distributed energy resources --- energy storage systems --- short term conditions --- cluster analysis (CA) --- nonlinear loads --- harmonics, cancellation, and attenuation of harmonics --- waveform distortion --- THDi --- low-voltage networks --- optimization techniques --- different batteries --- off-grid microgrid --- integrated renewable energy system --- cluster analysis --- K-means --- agglomerative --- ANFIS --- fuzzy logic --- induction generator --- MPPT --- neural network --- renewable energy --- variable speed WECS --- wind energy conversion system --- wind energy --- frequency estimation --- spectrum interpolation --- power network disturbances --- COVID-19 --- time-varying reproduction number --- social distancing --- load profile --- demographic characteristic --- household energy consumption --- demand-side management --- energy management --- time series --- Hidden Markov Model --- short-term forecast --- sparse signal decomposition --- supervised dictionary learning --- dictionary impulsion --- singular value decomposition --- discrete cosine transform --- discrete Haar transform --- discrete wavelet transform --- transient stability assessment --- home energy management --- binary-coded genetic algorithms --- optimal power scheduling --- demand response --- Data Injection Attack --- machine learning --- critical infrastructure --- smart grid --- water treatment plant --- power system --- virtual power plant (VPP) --- power quality (PQ) --- global index --- distributed energy resources (DER) --- energy storage systems (ESS) --- power systems --- long-term assessment --- battery energy storage systems (BESS) --- smart grids --- conducted disturbances --- power quality --- supraharmonics --- 2-150 kHz --- Power Line Communications (PLC) --- intentional emission --- non-intentional emission --- mains signalling --- virtual power plant --- data mining --- clustering --- distributed energy resources --- energy storage systems --- short term conditions --- cluster analysis (CA) --- nonlinear loads --- harmonics, cancellation, and attenuation of harmonics --- waveform distortion --- THDi --- low-voltage networks --- optimization techniques --- different batteries --- off-grid microgrid --- integrated renewable energy system --- cluster analysis --- K-means --- agglomerative --- ANFIS --- fuzzy logic --- induction generator --- MPPT --- neural network --- renewable energy --- variable speed WECS --- wind energy conversion system --- wind energy --- frequency estimation --- spectrum interpolation --- power network disturbances --- COVID-19 --- time-varying reproduction number --- social distancing --- load profile --- demographic characteristic --- household energy consumption --- demand-side management --- energy management --- time series --- Hidden Markov Model --- short-term forecast --- sparse signal decomposition --- supervised dictionary learning --- dictionary impulsion --- singular value decomposition --- discrete cosine transform --- discrete Haar transform --- discrete wavelet transform --- transient stability assessment --- home energy management --- binary-coded genetic algorithms --- optimal power scheduling --- demand response --- Data Injection Attack --- machine learning --- critical infrastructure --- smart grid --- water treatment plant --- power system

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This Special Issue was intended as a forum to advance research and apply machine-learning and data-mining methods to facilitate the development of modern electric power systems, grids and devices, and smart grids and protection devices, as well as to develop tools for more accurate and efficient power system analysis. Conventional signal processing is no longer adequate to extract all the relevant information from distorted signals through filtering, estimation, and detection to facilitate decision-making and control actions. Machine learning algorithms, optimization techniques and efficient numerical algorithms, distributed signal processing, machine learning, data-mining statistical signal detection, and estimation may help to solve contemporary challenges in modern power systems. The increased use of digital information and control technology can improve the grid’s reliability, security, and efficiency; the dynamic optimization of grid operations; demand response; the incorporation of demand-side resources and integration of energy-efficient resources; distribution automation; and the integration of smart appliances and consumer devices. Signal processing offers the tools needed to convert measurement data to information, and to transform information into actionable intelligence. This Special Issue includes fifteen articles, authored by international research teams from several countries.

Technology: general issues --- History of engineering & technology --- Energy industries & utilities --- virtual power plant (VPP) --- power quality (PQ) --- global index --- distributed energy resources (DER) --- energy storage systems (ESS) --- power systems --- long-term assessment --- battery energy storage systems (BESS) --- smart grids --- conducted disturbances --- power quality --- supraharmonics --- 2–150 kHz --- Power Line Communications (PLC) --- intentional emission --- non-intentional emission --- mains signalling --- virtual power plant --- data mining --- clustering --- distributed energy resources --- energy storage systems --- short term conditions --- cluster analysis (CA) --- nonlinear loads --- harmonics, cancellation, and attenuation of harmonics --- waveform distortion --- THDi --- low-voltage networks --- optimization techniques --- different batteries --- off-grid microgrid --- integrated renewable energy system --- cluster analysis --- K-means --- agglomerative --- ANFIS --- fuzzy logic --- induction generator --- MPPT --- neural network --- renewable energy --- variable speed WECS --- wind energy conversion system --- wind energy --- frequency estimation --- spectrum interpolation --- power network disturbances --- COVID-19 --- time-varying reproduction number --- social distancing --- load profile --- demographic characteristic --- household energy consumption --- demand-side management --- energy management --- time series --- Hidden Markov Model --- short-term forecast --- sparse signal decomposition --- supervised dictionary learning --- dictionary impulsion --- singular value decomposition --- discrete cosine transform --- discrete Haar transform --- discrete wavelet transform --- transient stability assessment --- home energy management --- binary-coded genetic algorithms --- optimal power scheduling --- demand response --- Data Injection Attack --- machine learning --- critical infrastructure --- smart grid --- water treatment plant --- power system --- n/a --- 2-150 kHz

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This Special Issue deals with the theory and applications of differential and difference equations, and includes papers for different branches of differential equations, such as - Boundary Value Problems for Fractional Differential Equations and Inclusions - Spectral Theory for Fractional Differential Equations - Generalized Abel's Integral Equations - Oscillation Results for Higher Order Differential Equations - Stability of Equilibria under Stochastic Perturbations - Harmonic Functions - Coincidence Continuation Theory for Multivalued Maps - Generalized Briot–Bouquet Differential Equation - Nonlocal Inverse Problem - Lyapunov Type Theorems for Exponential Stability - Fuzzy Functions on Time Scales - Modified Helmholtz Equation on a Regular Hexagon

Research & information: general --- Mathematics & science --- generating functions --- functional equations --- partial differential equations --- special numbers and polynomials --- Bernoulli numbers --- Euler numbers --- Stirling numbers --- Bell polynomials --- Cauchy numbers --- Poisson-Charlier polynomials --- Bernstein basis functions --- Daehee numbers and polynomials --- combinatorial sums --- binomial coefficients --- p-adic integral --- probability distribution --- Mittag-Leffler function --- spectrum --- eigenvalue --- fractional derivative --- q-Homotopy analysis transform method --- Natural decomposition method --- Whitham–Broer–Kaup equations --- Caputo derivative --- liner recursions --- convolution formulas --- Gegenbauer polynomials --- Humbert polynomials --- classical polynomials in several variables --- classical number sequences --- Riemann–Liouville fractional integral --- Mittag–Leffler function --- Babenko’s approach --- generalized Abel’s integral equation --- harmonic functions --- janowski functions --- starlike functions --- extreme points --- subordination --- ocillation --- higher-order --- differential equations --- p-Laplacian equations --- rumor spreading model --- white noise --- stochastic differential equations --- asymptotic mean square stability --- stability in probability --- linear matrix inequality --- Co-infection of HIV-TB --- equilibrium point --- reproduction number --- stability analysis --- backward bifurcation --- harmonic univalent functions --- generalized linear operator --- differential operator --- Salagean operator --- coefficient bounds --- essential maps --- coincidence points --- topological principles --- selections --- univalent function --- analytic function --- unit disk --- integro-differential equation --- mixed type equation --- spectral parameters --- integral conditions --- solvability --- exponential stability --- linear skew-product semiflows --- Lyapunov functions --- fractional differential equations --- fractional differential inclusions --- existence --- fixed point theorems --- fuzzy functions time scales --- Hukuhara difference --- generalized nabla Hukuhara derivative --- fuzzy nabla integral --- caputo fractional derivative --- multi-term fractional differential equations --- fixed point --- difference equations --- periodicity character --- nonexistence cases of periodic solutions --- hypersingular integral equations --- iterative projection method --- Lyapunov stability theory --- MADE --- eigenfunction --- convergence --- Fourier transform --- singular Cauchy problem --- asymptotic series --- regularization method --- turning point --- unified transform --- modified Helmholtz equation --- global relation --- triple q-hypergeometric function --- convergence region --- Ward q-addition --- q-integral representation --- generating functions --- functional equations --- partial differential equations --- special numbers and polynomials --- Bernoulli numbers --- Euler numbers --- Stirling numbers --- Bell polynomials --- Cauchy numbers --- Poisson-Charlier polynomials --- Bernstein basis functions --- Daehee numbers and polynomials --- combinatorial sums --- binomial coefficients --- p-adic integral --- probability distribution --- Mittag-Leffler function --- spectrum --- eigenvalue --- fractional derivative --- q-Homotopy analysis transform method --- Natural decomposition method --- Whitham–Broer–Kaup equations --- Caputo derivative --- liner recursions --- convolution formulas --- Gegenbauer polynomials --- Humbert polynomials --- classical polynomials in several variables --- classical number sequences --- Riemann–Liouville fractional integral --- Mittag–Leffler function --- Babenko’s approach --- generalized Abel’s integral equation --- harmonic functions --- janowski functions --- starlike functions --- extreme points --- subordination --- ocillation --- higher-order --- differential equations --- p-Laplacian equations --- rumor spreading model --- white noise --- stochastic differential equations --- asymptotic mean square stability --- stability in probability --- linear matrix inequality --- Co-infection of HIV-TB --- equilibrium point --- reproduction number --- stability analysis --- backward bifurcation --- harmonic univalent functions --- generalized linear operator --- differential operator --- Salagean operator --- coefficient bounds --- essential maps --- coincidence points --- topological principles --- selections --- univalent function --- analytic function --- unit disk --- integro-differential equation --- mixed type equation --- spectral parameters --- integral conditions --- solvability --- exponential stability --- linear skew-product semiflows --- Lyapunov functions --- fractional differential equations --- fractional differential inclusions --- existence --- fixed point theorems --- fuzzy functions time scales --- Hukuhara difference --- generalized nabla Hukuhara derivative --- fuzzy nabla integral --- caputo fractional derivative --- multi-term fractional differential equations --- fixed point --- difference equations --- periodicity character --- nonexistence cases of periodic solutions --- hypersingular integral equations --- iterative projection method --- Lyapunov stability theory --- MADE --- eigenfunction --- convergence --- Fourier transform --- singular Cauchy problem --- asymptotic series --- regularization method --- turning point --- unified transform --- modified Helmholtz equation --- global relation --- triple q-hypergeometric function --- convergence region --- Ward q-addition --- q-integral representation

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This Special Issue deals with the theory and applications of differential and difference equations, and includes papers for different branches of differential equations, such as - Boundary Value Problems for Fractional Differential Equations and Inclusions - Spectral Theory for Fractional Differential Equations - Generalized Abel's Integral Equations - Oscillation Results for Higher Order Differential Equations - Stability of Equilibria under Stochastic Perturbations - Harmonic Functions - Coincidence Continuation Theory for Multivalued Maps - Generalized Briot–Bouquet Differential Equation - Nonlocal Inverse Problem - Lyapunov Type Theorems for Exponential Stability - Fuzzy Functions on Time Scales - Modified Helmholtz Equation on a Regular Hexagon

generating functions --- functional equations --- partial differential equations --- special numbers and polynomials --- Bernoulli numbers --- Euler numbers --- Stirling numbers --- Bell polynomials --- Cauchy numbers --- Poisson-Charlier polynomials --- Bernstein basis functions --- Daehee numbers and polynomials --- combinatorial sums --- binomial coefficients --- p-adic integral --- probability distribution --- Mittag-Leffler function --- spectrum --- eigenvalue --- fractional derivative --- q-Homotopy analysis transform method --- Natural decomposition method --- Whitham–Broer–Kaup equations --- Caputo derivative --- liner recursions --- convolution formulas --- Gegenbauer polynomials --- Humbert polynomials --- classical polynomials in several variables --- classical number sequences --- Riemann–Liouville fractional integral --- Mittag–Leffler function --- Babenko’s approach --- generalized Abel’s integral equation --- harmonic functions --- janowski functions --- starlike functions --- extreme points --- subordination --- ocillation --- higher-order --- differential equations --- p-Laplacian equations --- rumor spreading model --- white noise --- stochastic differential equations --- asymptotic mean square stability --- stability in probability --- linear matrix inequality --- Co-infection of HIV-TB --- equilibrium point --- reproduction number --- stability analysis --- backward bifurcation --- harmonic univalent functions --- generalized linear operator --- differential operator --- Salagean operator --- coefficient bounds --- essential maps --- coincidence points --- topological principles --- selections --- univalent function --- analytic function --- unit disk --- integro-differential equation --- mixed type equation --- spectral parameters --- integral conditions --- solvability --- exponential stability --- linear skew-product semiflows --- Lyapunov functions --- fractional differential equations --- fractional differential inclusions --- existence --- fixed point theorems --- fuzzy functions time scales --- Hukuhara difference --- generalized nabla Hukuhara derivative --- fuzzy nabla integral --- caputo fractional derivative --- multi-term fractional differential equations --- fixed point --- difference equations --- periodicity character --- nonexistence cases of periodic solutions --- hypersingular integral equations --- iterative projection method --- Lyapunov stability theory --- MADE --- eigenfunction --- convergence --- Fourier transform --- singular Cauchy problem --- asymptotic series --- regularization method --- turning point --- unified transform --- modified Helmholtz equation --- global relation --- triple q-hypergeometric function --- convergence region --- Ward q-addition --- q-integral representation