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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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The results presented in this volume highlight some of the most recent advances in nanoscience and nanotechnology studies, from both the physical and chemical point of view, with an eye also to possible engineering applications. These studies demonstrate directly how effective, and at the same time stimulating is implementing the “crossfertilization” procedure. Indeed, multidisciplinary research allows one to catch more easily the analogies inherent different areas of science, as well as to take advantage and optimize different methods and techniques, often borrowed from other research areas.In the present Special Issue, we included six published papers. The latter contributions, on the one hand, are developed at the theory level and, on the other hand, show experimental results on the realization and experimental characterization of nanostructured systems, suitable for yielding progress towards the realization of systems and devices, that can ultimately lead to industrial applications. The results show that recent scientific research advances in these areas may provide important steps in the direction of fostering innovation and technological development.
chemical stability  reaction rate  chemical equilibria  fluctuation theory  kinetic theory  nanoparticles  thermal decomposition method  pyrolysis  laminar flow  graphene  annealing  doping  electric contacts  temperature dependence  HOPG  anion intercalation  blister  insitu AFM  electrodeposition process  group 1 metals  modeling  COMSOL Multiphysics  boron sheet  electronic structure  densityofstates (DoS)  Fermi curve  effective mass  chemical stability  graphene  temperature dependence in HOPG  electrodeposition process  boron sheet’s electronic structure
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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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Over the last years, sophisticated policy making propositions for sustainable rural and urban development have been recorded. The smart village and smart city concepts promote a humancentric vision for a new era of technologydriven social innovation. This Special Issue offers a useful overview of the most recent developments in the frequently overlapping fields of smart city and smart village research. A variety of topics including wellbeing, happiness, security, open democracy, open government, smart education, smart innovation, and migration have been addressed in this Special Issue. They define the direction for future research in both domains. The organization of the relevant debate is aligned around three pillars: Section A: Sustainable Smart City and Smart Village Research: Foundations • Clustering Smart City Services: Perceptions, Expectations, and Responses • Smart City Development and Residents’ WellBeing • Analysis of Social Networking Service Data for Smart Urban Planning Section B: Sustainable Smart City and Smart Village Research: Case Studies on Rethinking Security, Safety, Wellbeing, and Happiness • Exploring a StakeholderBased Urban Densification and Greening Agenda for Rotterdam Inner City—Accelerating the Transition to a Liveable Low Carbon City • The Impact of the Comprehensive Rural Village Development Program on Rural Sustainability in Korea • Analyzing the Level of Accessibility of Public Urban Green Spaces to Different Socially Vulnerable Groups of People • Consumers’ Preference and Factors Influencing Offal Consumption in the Amathole District Eastern Cape, South Africa • Sustainable Tourism: A Hidden Theory of the Cinematic Image? A Theoretical and Visual Analysis of the Way of St. James • Future Development of Taiwan’s Smart Cities from an Information Security Perspective • Towards a Smart and Sustainable City with the Involvement of Public Participation—The Case of Wroclaw Section C: Sustainable Smart City and Smart Village Research: Technical Issues • Detection and Localization of Water Leaks in Water Nets Supported by an ICT System with Artificial Intelligence Methods as a Way Forward for Smart Cities • A Study of the Public Landscape Order of Xinye Village • SpatioTemporal Changes and Dependencies of Land Prices: A Case Study of the City of Olomouc • Geographical Assessment of LowCarbon Transportation Modes: A Case Study from a Commuter University • Performance Analysis of a PollingBased Access Control Combined with the Sleeping Schema in V2I VANETs for Smart Cities.
synergetic urban landscape planning  low carbon cities  densification  liveability  greening  sustainable urban development  urban planning  policy evaluation  sustainable rural policy  spatial econometrics model  decomposition method  South Korea  lowcarbon transportation  walk  bike  transit  builtenvironment  perceptions  UNCG  Greensboro  North Carolina  offal  consumers  perception  consumption  meat quality  purchasepoint  pilgrimage and religion tourism  sustainable pilgrimage tourism  moviescapes  the Way of St. James  Accessibility  urban green space  social demand index  surface temperature  smart city  ecological wellbeing  population density  smallsized community  sustainable urban management  spatial equity  urban planning  smart city  information security  cloud computation security  big data information security  Internet of things information security  Smart Cities  social networks  ambient behavioral analysis  urban planning  decision making  sustainability  accessibility  land price map  landuse development  geographic information system  spatiotemporal changes  sustainability  Olomouc  city sustainable development  smart city implementation concept  residents’ participation  participatory budgeting  Wroclaw 1998–2018  smart cities  ICTS  energy efficiency  polling control  probability generating function  vehicular Adhoc networks (VANETs)  vehicletoinfrastructure (V2I)  water supply networks  network modelling  leak detection  artificial neural networks  settlement  culture  public landscape  landscape order  Xinye Village  smart city  usefulness experience  safety experience  convenience experience  SWB  smart cities  information and communication technologies  technology clusters  innovation transfer  sustainability  analytics  ICTs  policy making  smart cities  smart villages  smart urban applications  data mining  analytics  cloud computing and open source technologies  sustainability  entrepreneurship  economic growth  international migration  forced migration  smart technologies  ICT  open democracy  open government  smart education  smart innovation
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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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