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This book consists of nine papers covering a number of basic ideas, concepts, and methods of nonlinear analysis, as well as some current research problems. Thus, the reader is introduced to the fascinating theory around Brouwer's fixed point theorem, to Granas' theory of topological transversality, and to some advanced techniques of critical point theory and fixed point theory. Other topics include discontinuous differential equations, new results of metric fixed point theory, robust tracker design problems for various classes of nonlinear systems, and periodic solutions in computer virus propagation models.

Research & information: general --- Mathematics & science --- Krasnosel'skiĭ's fixed point theorem --- positive solutions --- discontinuous differential equations --- differential system --- p-Laplacian --- choquard equation --- nonhomogeneous --- nehari method --- minimax methods --- essential maps --- homotopy --- selections --- PID controller --- sliding mode control --- hybrid Taguchi real coded DNA algorithm --- perturbation estimator --- ℳ?-function --- ℳ?(λ)-function --- τ-function --- essential distance (e-distance) --- e0-metric --- Du-Hung's fixed point theorem --- Mizoguchi-Takahashi's fixed point theorem --- Nadler's fixed point theorem --- Banach contraction principle --- minimax --- multiplicity --- global minima --- Brouwer fixed point theorem --- Hamadard theorem --- Poincaré-miranda theorem --- nonlinear elliptic problem --- Robin boundary condition --- gradient dependence --- sub-supersolution --- positive solution --- periodic solutions --- SEIR-KS model --- computer virus model --- Krasnosel'skiĭ's fixed point theorem --- positive solutions --- discontinuous differential equations --- differential system --- p-Laplacian --- choquard equation --- nonhomogeneous --- nehari method --- minimax methods --- essential maps --- homotopy --- selections --- PID controller --- sliding mode control --- hybrid Taguchi real coded DNA algorithm --- perturbation estimator --- ℳ?-function --- ℳ?(λ)-function --- τ-function --- essential distance (e-distance) --- e0-metric --- Du-Hung's fixed point theorem --- Mizoguchi-Takahashi's fixed point theorem --- Nadler's fixed point theorem --- Banach contraction principle --- minimax --- multiplicity --- global minima --- Brouwer fixed point theorem --- Hamadard theorem --- Poincaré-miranda theorem --- nonlinear elliptic problem --- Robin boundary condition --- gradient dependence --- sub-supersolution --- positive solution --- periodic solutions --- SEIR-KS model --- computer virus model

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• Reference Manager
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This book consists of nine papers covering a number of basic ideas, concepts, and methods of nonlinear analysis, as well as some current research problems. Thus, the reader is introduced to the fascinating theory around Brouwer's fixed point theorem, to Granas' theory of topological transversality, and to some advanced techniques of critical point theory and fixed point theory. Other topics include discontinuous differential equations, new results of metric fixed point theory, robust tracker design problems for various classes of nonlinear systems, and periodic solutions in computer virus propagation models.

Research & information: general --- Mathematics & science --- Krasnosel’skiĭ’s fixed point theorem --- positive solutions --- discontinuous differential equations --- differential system --- p-Laplacian --- choquard equation --- nonhomogeneous --- nehari method --- minimax methods --- essential maps --- homotopy --- selections --- PID controller --- sliding mode control --- hybrid Taguchi real coded DNA algorithm --- perturbation estimator --- ℳ?-function --- ℳ?(λ)-function --- τ-function --- essential distance (e-distance) --- e0-metric --- Du-Hung’s fixed point theorem --- Mizoguchi-Takahashi’s fixed point theorem --- Nadler’s fixed point theorem --- Banach contraction principle --- minimax --- multiplicity --- global minima --- Brouwer fixed point theorem --- Hamadard theorem --- Poincaré–miranda theorem --- nonlinear elliptic problem --- Robin boundary condition --- gradient dependence --- sub-supersolution --- positive solution --- periodic solutions --- SEIR-KS model --- computer virus model --- n/a --- Krasnosel'skiĭ's fixed point theorem --- Du-Hung's fixed point theorem --- Mizoguchi-Takahashi's fixed point theorem --- Nadler's fixed point theorem --- Poincaré-miranda theorem

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During the past decades, the subject of calculus of integrals and derivatives of any arbitrary real or complex order has gained considerable popularity and impact. This is mainly due to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. In connection with this, great importance is attached to the publication of results that focus on recent and novel developments in the theory of any types of differential and fractional differential equation and inclusions, especially covering analytical and numerical research for such kinds of equations. This book is a compilation of articles from a Special Issue of Mathematics devoted to the topic of “Recent Investigations of Differential and Fractional Equations and Inclusions”. It contains some theoretical works and approximate methods in fractional differential equations and inclusions as well as fuzzy integrodifferential equations. Many of the papers were supported by the Bulgarian National Science Fund under Project KP-06-N32/7. Overall, the volume is an excellent witness of the relevance of the theory of fractional differential equations.

weakly upper semicontinuous --- essential maps --- homotopy --- Riemann-Liouville fractional differential equation --- delay --- lower and upper solutions --- monotone-iterative technique --- homoclinic solutions --- fourth-order p-Laplacian differential equations --- minimization theorem --- Clark’s theorem --- exponential dichotomy --- roughness --- asymptotically constant matrices --- double fuzzy Sumudu transform --- partial Volterra fuzzy integro-differential equations --- n-th order fuzzy partial H-derivative --- m-dissipative operators --- limit solutions --- integral solutions --- one-sided Perron condition --- Banach spaces --- fixed point --- complete metric space --- fractional differential equations --- optimal feedback control --- Voigt model --- alpha-model --- fractional derivative --- Riemann–Liouville fractional differential equations --- nonlocal boundary conditions --- positive solutions --- existence --- multiplicity --- Caputo derivative --- Riemann–Liouville integral --- multipoint and sub-strip boundary conditions --- fixed point theorem --- fractional Navier–Stokes equations --- variable delay --- modified fractional Halanay inequality --- generalized comparison principle --- dissipativity --- Fourier-Laplace transforms --- porous material --- eigenvalues method --- fractional time derivative

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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

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