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proximity point  rectangular metric  Gcontraction  graph  fixed point  Geraghty  bmetric space  diffeomorphism  contactomorphism  symplectomorphism  common fixed point  binary relation  preserving mapping  (?g,
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This issue is a continuation of the previous successful Special Issue “Mathematical Analysis and Applications”
common fixed point  metriclike space  ?Geraghty contraction  triangular ?admissible mapping  fixed circle  common fixed circle  fixedcircle theorem  extended partial Sbmetric spaces  Sbmetric spaces  fixed point  generalized hypergeometric functions  Gauss and confluent hypergeometric functions  summation theorems of hypergeometric functions  partial symmetric  fixed point  contraction and weak contraction  Nadler’s theorem  linear elastostatics  simple layer potentials  displacement problem  existence and uniqueness theorems  Fredholm alternative  singular data  differential equations  Sheffer polynomial sets  generating functions  monomiality principle  quasi metric space  Suzuki contractions  fixed point theorems  modified ?distance  almost perfect functions  generating function  series transformation  gamma function  Hankel contour  Fermi–Dirac function  Bose–Einstein function  Weyl transform  series representation  Hermite–Hadamard inequalities  (p, q)derivative  (p, q)integral  convex functions  fixed point  Reich contraction  Hardy–Rogers contraction  almost bmetric space  additive (Cauchy) equation  additive mapping  Hyers–Ulam stability  generalized Hyers–Ulam stability  hyperstability  bounded index  bounded Lindex in direction  slice function  entire function  bounded lindex  generalized hypergeometric functions  classical summation theorems  generalization  laplace transforms  gamma and beta functions  SzászMirakjan operators  SzászMirakjan Beta type operators  extended Gamma and Beta functions  confluent hypergeometric function  Modulus of smoothness  modulus of continuity  Lipschitz class  local approximation  Voronovskaja type approximation theorem  operators theory 44A99, 47B99, 47A62  special functions 33C52, 33C65, 33C99, 33B10, 33B15  Stirling numbers and Touchard polynomials 11B73  n/a
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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 reallife 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.
Legendre wavelets  collocation method  threestep Taylor method  asymptotic stability  timedependent partial differential equations  noninstantaneous impulses  Caputo fractional derivative  differential equations  state dependent delays  lipschitz stability  limitperiodic solutions  difference equations  exponential dichotomy  strong nonlinearities  effective existence criteria  population dynamics  discrete Lyapunov equation  difference equations  Hilbert space  dichotomy  exponential stability  ?Laplacian operator  mean curvature operator  heteroclinic solutions  problems in the real line  lower and upper solutions  Nagumo condition on the real line  fixed point theory  coupled nonlinear systems  functional boundary conditions  Schauder’s fixed point theory  Arzèla Ascoli theorem  lower and upper solutions  first order periodic systems  SIRS epidemic model  mathematical modelling  Navier–Stokes equations  global solutions  regular solutions  a priori estimates  weak solutions  kinetic energy  dissipation  Bäcklund transformation  Clairin’s method  generalized Liouville equation  Miura transformation  Kortewegde Vries equation  secondorder differential/difference/qdifference equation of hypergeometric type  nonuniform lattices  divideddifference equations  polynomial solution  integrodifferentials  Sumudu decomposition method  dynamical system
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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 qdifference equation  existence and uniqueness  positive solutions  fixed point theorem on mixed monotone operators  fractional pLaplacian  Kirchhofftype equations  fountain theorem  modified functional methods  Moser iteration method  fractionalorder neural networks  delays  distributed delays  impulses  Mittag–Leffler synchronization  Lyapunov functions  Razumikhin method  generalized convexity  bvex functions  subbsconvex functions  oscillation  nonlinear differential system  delay differential system  ?fractional derivative  positive solution  fractional thermostat model  fixed point index  dependence on a parameter  Hermite–Hadamard’s Inequality  Convex Functions  Powermean Inequality  Jenson Integral Inequality  Riemann—Liouville Fractional Integration  Laplace Adomian Decomposition Method (LADM)  NavierStokes equation  Caputo Operator  fractionalorder system  model order reduction  controllability and observability Gramians  energy inequality  integral conditions  fractional wave equation  existence and uniqueness  initial boundary value problem  conformable fractional derivative  conformable partial fractional derivative  conformable double Laplace decomposition method  conformable Laplace transform  singular one dimensional coupled Burgers’ equation
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In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: selfexcited attractors and hidden attractors. The localization of selfexcited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with nonhyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phaselocked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with selfexcited attractors and hidden attractors.
new chaotic system  multiple attractors  electronic circuit realization  SBox algorithm  chaotic systems  circuit design  parameter estimation  optimization methods  Gaussian mixture model  chaotic system  empirical mode decomposition  permutation entropy  image encryption  hidden attractors  fixed point  stability  nonlinear transport equation  stochastic (strong) entropy solution  uniqueness  existence  multiscale multivariate entropy  multistability  selfreproducing system  chaos  hidden attractor  selfexcited attractor  fractional order  spectral entropy  coexistence  multistability  chaotic flow  hidden attractor  multistable  entropy  core entropy  Thurston’s algorithm  Hubbard tree  external rays  chaos  Lyapunov exponents  multiplevalued  static memory  strange attractors  fractional discrete chaos  entropy  projective synchronization  full state hybrid projective synchronization  generalized synchronization  inverse full state hybrid projective synchronization  inverse generalized synchronization  multichannel supply chain  service game  chaos  entropy  BOPS  Hopf bifurcation  selfexcited attractors  multistability  sample entropy  PRNG  Nonequilibrium fourdimensional chaotic system  entropy measure  adaptive approximatorbased control  neural network  uncertain dynamics  synchronization  fractionalorder  complexvariable chaotic system  unknown complex parameters  chaotic map  fixed point  chaos  approximate entropy  implementation  hidden attractor  hyperchaotic system  multistability  entropy analysis  hidden attractor  complex systems  fractionalorder  entropy  chaotic maps  chaos  spatial dynamics  Bogdanov Map  chaos  laser  resonator
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Following the tremendous reception of our first volume on topological groups called ""Topological Groups: Yesterday, Today, and Tomorrow"", we now present our second volume. Like the first volume, this collection contains articles by some of the best scholars in the world on topological groups. A feature of the first volume was surveys, and we continue that tradition in this volume with three new surveys. These surveys are of interest not only to the expert but also to those who are less experienced. Particularly exciting to active researchers, especially young researchers, is the inclusion of over three dozen open questions. This volume consists of 11 papers containing many new and interesting results and examples across the spectrum of topological group theory and related topics. Wellknown researchers who contributed to this volume include Taras Banakh, Michael Megrelishvili, Sidney A. Morris, Saharon Shelah, George A. Willis, O'lga V. Sipacheva, and Stephen Wagner.
descriptive set theory  polish group topologies  rightangled Artin groups  topological group  paratopological group  topological semigroup  absolutely closed topological group  topological group of compact exponent  locally compact group  endomorphism  scale  tree  Neretin’s group  Thompson’s group  padic Lie group  large set in a group  vast set  syndetic set  thick set  piecewise syndetic set  Boolean topological group  arrow ultrafilter  Ramsey ultrafilter  coarse structure  coarse space  ballean  varieties of coarse spaces  space of closed subgroups  Chabauty topology  Vietoris topology  Bourbaki uniformity  Gromov’s compactification  group representation  matrix coefficient  semigroup compactification  tame function  dynamical system  continuous inverse algebra  character  maximal ideal  fixed point algebra  extension  pseudocompact  strongly pseudocompact  pcompact  selectively sequentially pseudocompact  pseudo?bounded  nontrivial convergent sequence  separable  free precompact Boolean group  reflexive group  maximal space  ultrafilter space  topological group  Lie group  compact topological semigroup  Hspace  mapping cylinder  fibre bundle  separable topological group  subgroup  product  isomorphic embedding  quotient group  free topological group
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A plethora of problems from diverse disciplines such as Mathematics, Mathematical: Biology, Chemistry, Economics, Physics, Scientific Computing and also Engineering can be formulated as an equation defined in abstract spaces using Mathematical Modelling. The solutions of these equations can be found in closed form only in special case. That is why researchers and practitioners utilize iterative procedures from which a sequence is being generated approximating the solution under some conditions on the initial data. This type of research is considered most interesting and challenging. This is our motivation for the introduction of this special issue on Iterative Procedures.
Banach space  weightedNewton method  local convergence  Fréchetderivative  ball radius of convergence  Nondifferentiable operator  nonlinear equation  divided difference  Lipschitz condition  convergence order  local and semilocal convergence  scalar equations  computational convergence order  Steffensen’s method  basins of attraction  nonlinear equations  multipleroot solvers  Traub–Steffensen method  fast algorithms  Multiple roots  Optimal iterative methods  Scalar equations  Order of convergence  simple roots  Newton’s method  computational convergence order  nonlinear equations  split variational inclusion problem  generalized mixed equilibrium problem  fixed point problem  maximal monotone operator  left Bregman asymptotically nonexpansive mapping  uniformly convex and uniformly smooth Banach space  nonlinear equations  multiple roots  derivativefree method  optimal convergence  multiple roots  optimal iterative methods  scalar equations  order of convergence  Newton–HSS method  systems of nonlinear equations  semilocal convergence  local convergence  convergence order  Banach space  iterative method  nonlinear equations  Chebyshev’s iterative method  fractional derivative  basin of attraction  nonlinear equations  iterative methods  general means  basin of attraction
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Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a nontrivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.
point projection  intersection  parametric curve  ndimensional Euclidean space  Newton’s second order method  fixed point theorem  nonlinear equations  multiple zeros  optimal iterative methods  higher order of convergence  nonlinear operator equation  Fréchet derivative  ?continuity condition  Newtonlike method  Frédholm integral equation  nonlinear equations  Padé approximation  iterative method  order of convergence  numerical experiment  fourth order iterative methods  local convergence  banach space  radius of convergence  nonlinear equation  iterative process  nondifferentiable operator  Lipschitz condition  high order  sixteenth order convergence method  local convergence  dynamics  Banach space  Newton’s method  semilocal convergence  Kantorovich hypothesis  iterative methods  Steffensen’s method  Rorder  with memory  computational efficiency  nonlinear equation  basins of attraction  optimal order  higher order method  computational order of convergence  nonlinear equations  multiple roots  Chebyshev–Halleytype  optimal iterative methods  efficiency index  Banach space  semilocal convergence  ?continuity condition  Jarratt method  error bound  Fredholm integral equation  Newton’s method  global convergence  variational inequality problem  split variational inclusion problem  multivalued quasinonexpasive mappings  Hilbert space  sixteenthorder optimal convergence  multipleroot finder  asymptotic error constant  weight function  purely imaginary extraneous fixed point  attractor basin  drazin inverse  generalized inverse  iterative methods  higher order  efficiency index  integral equation  efficiency index  nonlinear models  iterative methods  higher order  nonlinear equations  optimal iterative methods  multiple roots  efficiency index  iterative methods  nonlinear equations  Newtontype methods  smooth and nonsmooth operators  heston model  Hull–White  option pricing  PDE  finite difference (FD)  iteration scheme  Moore–Penrose  rectangular matrices  rate of convergence  efficiency index  nonlinear equations  conjugate gradient method  projection method  convex constraints  signal and image processing  nonlinear monotone equations  conjugate gradient method  projection method  signal processing  nonlinear systems  multipoint iterative methods  divided difference operator  order of convergence  Newton’s method  computational efficiency index  system of nonlinear equations  Newton method  NewtonHSS method  nonlinear HSSlike method  PicardHSS method  convexity  least square problem  accretive operators  signal processing  point projection  intersection  planar algebraic curve  Newton’s iterative method  the improved curvature circle algorithm  systems of nonlinear equations  King’s family  order of convergence  multipoint iterative methods  nonlinear equations  Potra–Pták method  optimal methods  weight function  basin of attraction  engineering applications  Kung–Traub conjecture  multipoint iterations  nonlinear equation  optimal order  basins of attraction
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Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences.
highly oscillatory  convolution quadrature rule  volterra integral equation  Bessel kernel  convergence  higher order Schwarzian derivatives  Janowski starlike function  Janowski convex function  bound on derivatives  tangent numbers  tangent polynomials  Carlitztype qtangent numbers  Carlitztype qtangent polynomials  (p,q)analogue of tangent numbers and polynomials  (p,q)analogue of tangent zeta function  symmetric identities  zeros  Lommel functions  univalent functions  starlike functions  convex functions  inclusion relationships  analytic function  Hankel determinant  exponential function  upper bound  nonlinear boundary value problems  fractionalorder differential equations  RiemannStieltjes functional integral  LiouvilleCaputo fractional derivative  infinitepoint boundary conditions  advanced and deviated arguments  existence of at least one solution  Fredholm integral equation  Schauder fixed point theorem  Hölder condition  generalized Kuramoto–Sivashinsky equation  modified Kudryashov method  exact solutions  Maple graphs  analytic function  Hadamard product (convolution)  partial sum  Srivastava–Tomovski generalization of Mittag–Leffler function  subordination  differential equation  differential inclusion  Liouville–Caputotype fractional derivative  fractional integral  existence  fixed point  Bernoulli spiral  Grandi curves  Chebyshev polynomials  pseudoChebyshev polynomials  orthogonality property  symmetric  encryption  password  hash  cryptography  PBKDF  q–Bleimann–Butzer–Hahn operators  (p,q)integers  (p,q)Bernstein operators  (p,q)Bleimann–Butzer–Hahn operators  modulus of continuity  rate of approximation  Kfunctional  HurwitzLerch zeta function  generalized functions  analytic number theory  ?generalized HurwitzLerch zeta functions  derivative properties  series representation  basic hypergeometric functions  generating functions  qpolynomials  analytic functions  Mittag–Leffler functions  starlike functions  convex functions  Hardy space  vibrating string equation  initial conditions  spectral decomposition  regular solution  the uniqueness of the solution  the existence of a solution  analytic  ?convex function  starlike function  stronglystarlike function  subordination  q Sheffer–Appell polynomials  generating relations  determinant definition  recurrence relation  q Hermite–Bernoulli polynomials  q Hermite–Euler polynomials  q Hermite–Genocchi polynomials  Volterra integral equations  highly oscillatory Bessel kernel  Hermite interpolation  direct Hermite collocation method  piecewise Hermite collocation method  differential operator  qhypergeometric functions  meromorphic function  Mittag–Leffler function  Hadamard product  differential subordination  starlike functions  Bell numbers  radius estimate  (p, q)integers  Dunkl analogue  generating functions  generalization of exponential function  Szász operator  modulus of continuity  function spaces and their duals  distributions  tempered distributions  Schwartz testing function space  generalized functions  distribution space  wavelet transform of generalized functions  Fourier transform  analytic function  subordination  Dziok–Srivastava operator  nonlinear boundary value problem  nonlocal  multipoint  multistrip  existence  Ulam stability  functions of bounded boundary and bounded radius rotations  subordination  functions with positive real part  uniformly starlike and convex functions  analytic functions  univalent functions  starlike and qstarlike functions  qderivative (or qdifference) operator  sufficient conditions  distortion theorems  Janowski functions  analytic number theory  ?generalized Hurwitz–Lerch zeta functions  derivative properties  recurrence relations  integral representations  Mellin transform  natural transform  Adomian decomposition method  Caputo fractional derivative  generalized mittagleffler function  analytic functions  Hadamard product  starlike functions  qderivative (or qdifference) operator  Hankel determinant  qstarlike functions  fuzzy volterra integrodifferential equations  fuzzy general linear method  fuzzy differential equations  generalized Hukuhara differentiability  spectrum symmetry  DCT  MFCC  audio features  anuran calls  analytic functions  convex functions  starlike functions  strongly convex functions  strongly starlike functions  uniformly convex functions  Struve functions  truncatedexponential polynomials  monomiality principle  generating functions  Apostoltype polynomials and Apostoltype numbers  Bernoulli, Euler and Genocchi polynomials  Bernoulli, Euler, and Genocchi numbers  operational methods  summation formulas  symmetric identities  Euler numbers and polynomials  qEuler numbers and polynomials  HurwitzEuler eta function  multiple HurwitzEuler eta function  higher order qEuler numbers and polynomials  (p, q)Euler numbers and polynomials of higher order  symmetric identities  symmetry of the zero
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The everincreasing need for higher efficiency, smaller size, and lower cost make the analysis, understanding, and design of energy conversion systems extremely important, interesting, and even imperative. One of the most neglected features in the study of such systems is the effect of the inherent nonlinearities on the stability of the system. Due to these nonlinearities, these devices may exhibit undesirable and complex dynamics, which are the focus of many researchers. Even though a lot of research has taken place in this area during the last 20 years, it is still an active research topic for mainstream power engineers. This research has demonstrated that these systems can become unstable with a direct result in increased losses, extra subharmonics, and even uncontrollability/unobservability. The detailed study of these systems can help in the design of smaller, lighter, and less expensive converters that are particularly important in emerging areas of research like electric vehicles, smart grids, renewable energy sources, and others. The aim of this Special Issue is to cover control and nonlinear aspects of instabilities in different energy conversion systems: theoretical, analysis modelling, and practical solutions for such emerging applications. In this Special Issue, we present novel research works in different areas of the control and nonlinear dynamics of energy conversion systems.
datadriven  prediction  neural network  airhandling unit (AHU)  supply air temperature  pulverizing system  soft sensor  inferential control  moving horizon estimation  multimodel predictive control  microgrid  droop control  virtual impedance  harmonic suppression  power quality  combined heat and power unit  twostage bypass  dynamic model  coordinated control system  predictive control  decoupling control  power conversion  model–plant mismatches  disturbance observer  performance recovery  offsetfree  electrical machine  electromagnetic vibration  multiphysics  rotor dynamics  air gap eccentricity  calculation method  magnetic saturation  corrugated pipe  whistling noise  Helmholtz number  excited modes  switched reluctance generator  capacitance current pulse train control  voltage ripple  capacitance current  feedback coefficient  distributed architecture  maximum power point tracking  sliding mode control  overvoltage  permanent magnet synchronous motor (PMSM)  single artificial neuron goal representation heuristic dynamic programming (SANGrHDP)  single artificial neuron (SAN)  reinforcement learning (RL)  goal representation heuristic dynamic programming (GrHDP)  adaptive dynamic programming (ADP)  sliding mode observer (SMO)  permanent magnet synchronous motor (PMSM)  extended back electromotive force (EEMF)  position sensorless  bridgeless converter  discontinuous conduction mode (DCM)  high stepup voltage gain  power factor correction (PFC)  space mechanism  multiclearance  nonlinear dynamic model  planetary gears  vibration characteristics  new stepup converter  ultrahigh voltage conversion ratio  smallsignal model  averagecurrent mode control  slope compensation  monodromy matrix  current mode control  boostflyback converter  explosionmagnetic generator  plasma accelerator  currentpulse formation  DCDC buck converter  contraction analysis  global stability  matrix norm  DC micro grid  efficiency optimization  variable bus voltage MG  variable switching frequency DCDC converters  centralized vs. decentralized control  local vs. global optimization  buck converter  DC motor  bifurcations in control parameter  sliding control  zero average dynamics  fixedpoint inducting control  DCDC converters  quadratic boost  maximum power point tracking (MPPT)  nonlinear dynamics  subharmonic oscillations  photovoltaic (PV)  steel catenary riser  rigid body rotation  wave  the load of suspension point in the z direction  Cable3D
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