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In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Niet-lineaire systemen. --- Nonlinear systems -- Mathematical models. --- Optimaliseren. --- Lyapunov functions. --- Differential equations.

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This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses). At the present time the qualitative theory of such equations is under rapid development. After a presentation of the fundamental theory of existence, uniqueness and continuability of solutions, a systematic development of stability theory for that class of problems is given which makes the book unique. It addresses to a wide audience such as mathematicians, applied research

Impulsive differential equations. --- Stability. --- Lyapunov functions. --- Functions, Liapunov --- Liapunov functions --- Differential equations --- Dynamics --- Mechanics --- Motion --- Vibration --- Benjamin-Feir instability --- Equilibrium --- Impulse differential equations --- Impulsive partial differential equations --- Differential equations, Partial --- Functional Differential Equations. --- Ljapunov Stability. --- Ordinary Differential Equations. --- Stability Theory.

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The basin of attraction of an equilibrium of an ordinary differential equation can be determined using a Lyapunov function. A new method to construct such a Lyapunov function using radial basis functions is presented in this volume intended for researchers and advanced students from both dynamical systems and radial basis functions. Besides an introduction to both areas and a detailed description of the method, it contains error estimates and many examples.

Lyapunov functions. --- Radial basis functions. --- Electronic books. -- local. --- Lyapunov functions --- Radial basis functions --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Applied Mathematics --- Calculus --- Mathematical Theory --- Basis functions, Radial --- Functions, Radial basis --- Radial basis function method --- Functions, Liapunov --- Liapunov functions --- Mathematics. --- Approximation theory. --- Dynamics. --- Ergodic theory. --- Differential equations. --- Dynamical Systems and Ergodic Theory. --- Approximations and Expansions. --- Ordinary Differential Equations. --- 517.91 Differential equations --- Differential equations --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Math --- Science --- Approximation theory --- Differentiable dynamical systems. --- Differential Equations. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics

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Fractional calculus provides the possibility of introducing integrals and derivatives of an arbitrary order in the mathematical modelling of physical processes, and it has become a relevant subject with applications to various fields, such as anomalous diffusion, propagation in different media, and propogation in relation to materials with different properties. However, many aspects from theoretical and practical points of view have still to be developed in relation to models based on fractional operators. This Special Issue is related to new developments on different aspects of fractional differential equations, both from a theoretical point of view and in terms of applications in different fields such as physics, chemistry, or control theory, for instance. The topics of the Issue include fractional calculus, the mathematical analysis of the properties of the solutions to fractional equations, the extension of classical approaches, or applications of fractional equations to several fields.

fractional wave equation --- dependence on a parameter --- conformable double Laplace decomposition method --- Riemann—Liouville Fractional Integration --- Lyapunov functions --- Power-mean Inequality --- modified functional methods --- oscillation --- fractional-order neural networks --- initial boundary value problem --- fractional p-Laplacian --- model order reduction --- ?-fractional derivative --- Convex Functions --- existence and uniqueness --- conformable partial fractional derivative --- nonlinear differential system --- conformable Laplace transform --- Mittag–Leffler synchronization --- delays --- controllability and observability Gramians --- impulses --- conformable fractional derivative --- Moser iteration method --- fractional q-difference equation --- energy inequality --- b-vex functions --- Navier-Stokes equation --- fractional-order system --- Kirchhoff-type equations --- Razumikhin method --- Laplace Adomian Decomposition Method (LADM) --- fountain theorem --- Hermite–Hadamard’s Inequality --- distributed delays --- Caputo Operator --- fractional thermostat model --- sub-b-s-convex functions --- fixed point theorem on mixed monotone operators --- singular one dimensional coupled Burgers’ equation --- generalized convexity --- delay differential system --- positive solutions --- positive solution --- fixed point index --- Jenson Integral Inequality --- integral conditions

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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