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Metric fixed-point theory lies in the intersection of three main subjects: topology, functional analysis, and applied mathematics. The first fixed-point theorem, also known as contraction mapping principle, was abstracted by Banach from the papers of Liouville and Picard, in which certain differential equations were solved by using the method of successive approximation. In other words, fixed-point theory developed from applied mathematics and has developed in functional analysis and topology. Fixed-point theory is a dynamic research subject that has never lost the attention of researchers, as it is very open to development both in theoretical and practical fields. In this Special Issue, among several submissions, we selected eight papers that we believe will be interesting to researchers who study metric fixed-point theory and related applications. It is great to see that this Special Issue fulfilled its aims. There are not only theoretical results but also some applications that were based on obtained fixed-point results. In addition, the presented results have great potential to be improved, extended, and generalized in distinct ways. The published results also have a wide application potential in various qualitative sciences, including physics, economics, computer science, engineering, and so on.

b-metric --- Banach fixed point theorem --- Caristi fixed point theorem --- homotopy --- M-metric --- M-Pompeiu–Hausdorff type metric --- multivalued mapping --- fixed point --- quasi metric space --- altering distance function --- (ψ, ϕ)-quasi contraction. --- pata type contraction --- Suzuki type contraction --- C-condition --- orbital admissible mapping --- non-Archimedean quasi modular metric space --- θ-contraction --- Suzuki contraction --- simulation contraction --- R-function --- simulation function --- manageable function --- contractivity condition --- binary relation --- quasi-metric space --- left K-complete --- α–ψ-contractive mapping --- asymptotic stability --- differential and riemann-liouville fractional differential neutral systems --- linear matrix inequality

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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

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Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.

Robust optimization. --- Linear programming. --- 519.8 --- 681.3*G16 --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 519.8 Operational research --- Operational research --- Robust optimization --- Linear programming --- Optimisation robuste --- Programmation linéaire --- Optimization, Robust --- RO (Robust optimization) --- Mathematical optimization --- Production scheduling --- Programming (Mathematics) --- 0O. --- Accuracy and precision. --- Additive model. --- Almost surely. --- Approximation algorithm. --- Approximation. --- Best, worst and average case. --- Bifurcation theory. --- Big O notation. --- Candidate solution. --- Central limit theorem. --- Chaos theory. --- Coefficient. --- Computational complexity theory. --- Constrained optimization. --- Convex hull. --- Convex optimization. --- Convex set. --- Cumulative distribution function. --- Curse of dimensionality. --- Decision problem. --- Decision rule. --- Degeneracy (mathematics). --- Diagram (category theory). --- Duality (optimization). --- Dynamic programming. --- Exponential function. --- Feasible region. --- Floor and ceiling functions. --- For All Practical Purposes. --- Free product. --- Ideal solution. --- Identity matrix. --- Inequality (mathematics). --- Infimum and supremum. --- Integer programming. --- Law of large numbers. --- Likelihood-ratio test. --- Linear dynamical system. --- Linear inequality. --- Linear map. --- Linear matrix inequality. --- Linear regression. --- Loss function. --- Margin classifier. --- Markov chain. --- Markov decision process. --- Mathematical optimization. --- Max-plus algebra. --- Maxima and minima. --- Multivariate normal distribution. --- NP-hardness. --- Norm (mathematics). --- Normal distribution. --- Optimal control. --- Optimization problem. --- Orientability. --- P versus NP problem. --- Pairwise. --- Parameter. --- Parametric family. --- Probability distribution. --- Probability. --- Proportionality (mathematics). --- Quantity. --- Random variable. --- Relative interior. --- Robust control. --- Robust decision-making. --- Semi-infinite. --- Sensitivity analysis. --- Simple set. --- Singular value. --- Skew-symmetric matrix. --- Slack variable. --- Special case. --- Spherical model. --- Spline (mathematics). --- State variable. --- Stochastic calculus. --- Stochastic control. --- Stochastic optimization. --- Stochastic programming. --- Stochastic. --- Strong duality. --- Support vector machine. --- Theorem. --- Time complexity. --- Uncertainty. --- Uniform distribution (discrete). --- Unimodality. --- Upper and lower bounds. --- Variable (mathematics). --- Virtual displacement. --- Weak duality. --- Wiener filter. --- With high probability. --- Without loss of generality.

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The most influential research topic in the twenty-first century seems to be mathematics, as it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. Therefore, the intention of this Special Issue is to deal with mathematical works related to engineering and multidisciplinary problems. Modern developments in theoretical and applied science have widely depended our knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges in the theory and applications of fractional calculus in engineering sciences. The special issue included some original research articles that address significant issues and contribute towards the development of new concepts, methodologies, applications, trends and knowledge in mathematics. Potential topics include, but are not limited to, the following: Fractional mathematical models; Computational methods for the fractional PDEs in engineering; New mathematical approaches, innovations and challenges in biotechnologies and biomedicine; Applied mathematics; Engineering research based on advanced mathematical tools.

Technology: general issues --- History of engineering & technology --- fractional order IMC --- first order plus dead-time processes --- event-based implementation --- numerical simulations --- comparative closed loop results --- nonlinear wave phenomen --- RBF --- local RBF-FD --- stability --- unmanned aerial vehicle (UAV) --- quaternion-based estimator --- low-cost design --- automatic optical inspection --- kinetic theory --- parallel robots --- robust control --- sliding mode control --- basinI --- basinII --- mean pressure head --- pressure head with different probabilities of occurrence --- standard deviation of the pressure fluctuations --- statistical modeling --- USBR --- desalination --- humidification-dehumidification --- waste heat recovery --- mathematical model --- yearly analysis --- thermo-economics --- multi-objective optimization --- cruise altitude --- fuel consumption --- time to climb --- Hermite-Simpson method --- trajectory optimization --- terminal residual analysis (TRA) --- m-σ terminal residual analysis (m-σ TRA) --- power transformer --- stray losses --- analytical methods --- finite element method --- gridshell structures --- shape ratio --- length ratio --- regularity --- particle swarm optimization --- genetic algorithm --- hybrid nanofluid --- dual solutions --- mixed convection --- stagnation point --- radiation --- stability analysis --- machine learning --- eXterme Gradient Boosting --- Computation Fluid Dynamics --- blade vibration --- unsteady aerodynamic model --- active disturbance rejection control (ADRC) --- multiobjective optimization --- time delay systems --- tuning rules --- soft robotics --- fractional calculus --- CACSD toolbox --- operating point linearization --- automatic uncertainty bound computation --- Model-in-the-Loop simulation --- hybrid simulation --- ℋ∞ control --- μ synthesis --- DC-to-DC power converters --- buck --- boost --- SEPIC --- rainfall-runoff model --- curve number --- inferential statistics --- 3D runoff difference model --- model calibration --- PAT model --- modified affinity laws --- hydraulic simulation tool --- μ-synthesis --- fractional-order control --- swarm optimization --- artificial bee colony optimization --- CNC machine --- mixed sensitivity --- D–K iteration --- Linear Matrix Inequality --- biotechnology --- fermentation process --- batch bioreactors --- modeling --- control system design and synthesis --- linear control --- adaptive control --- model reference adaptive control --- control system realization --- mixed-sensitivity --- FO-PID --- twin rotor aerodynamic system

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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