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It is very well known that differential equations are related with the rise of physical science in the last several decades and they are used successfully for models of real-world problems in a variety of fields from several disciplines. Additionally, difference equations represent the discrete analogues of differential equations. These types of equations started to be used intensively during the last several years for their multiple applications, particularly in complex chaotic behavior. A certain class of differential and related difference equations is represented by their respective fractional forms, which have been utilized to better describe non-local phenomena appearing in all branches of science and engineering. The purpose of this book is to present some common results given by mathematicians together with physicists, engineers, as well as other scientists, for whom differential and difference equations are valuable research tools. The reported results can be used by researchers and academics working in both pure and applied differential equations.

Research & information: general --- Mathematics & science --- dynamic equations --- time scales --- classification --- existence --- necessary and sufficient conditions --- fractional calculus --- triangular fuzzy number --- double-parametric form --- FRDTM --- fractional dynamical model of marriage --- approximate controllability --- degenerate evolution equation --- fractional Caputo derivative --- sectorial operator --- fractional symmetric Hahn integral --- fractional symmetric Hahn difference operator --- Arrhenius activation energy --- rotating disk --- Darcy–Forchheimer flow --- binary chemical reaction --- nanoparticles --- numerical solution --- fractional differential equations --- two-dimensional wavelets --- finite differences --- fractional diffusion-wave equation --- fractional derivative --- ill-posed problem --- Tikhonov regularization method --- non-linear differential equation --- cubic B-spline --- central finite difference approximations --- absolute errors --- second order differential equations --- mild solution --- non-instantaneous impulses --- Kuratowski measure of noncompactness --- Darbo fixed point --- multi-stage method --- multi-step method --- Runge–Kutta method --- backward difference formula --- stiff system --- numerical solutions --- Riemann-Liouville fractional integral --- Caputo fractional derivative --- fractional Taylor vector --- kerosene oil-based fluid --- stagnation point --- carbon nanotubes --- variable thicker surface --- thermal radiation --- differential equations --- symmetric identities --- degenerate Hermite polynomials --- complex zeros --- oscillation --- third order --- mixed neutral differential equations --- powers of stochastic Gompertz diffusion models --- powers of stochastic lognormal diffusion models --- estimation in diffusion process --- stationary distribution and ergodicity --- trend function --- application to simulated data --- n-th order linear differential equation --- two-point boundary value problem --- Green function --- linear differential equation --- exponential stability --- linear output feedback --- stabilization --- uncertain system --- nonlocal effects --- linear control system --- Hilbert space --- state feedback control --- exact controllability --- upper Bohl exponent

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Over the past four decades, there has been increased attention given to the research of fluid mechanics due to its wide application in industry and phycology. Major advances in the modeling of key topics such Newtonian and non-Newtonian fluids and thin film flows have been made and finally published in the Special Issue of coatings. This is an attempt to edit the Special Issue into a book. Although this book is not a formal textbook, it will definitely be useful for university teachers, research students, industrial researchers and in overcoming the difficulties occurring in the said topic, while dealing with the nonlinear governing equations. For such types of equations, it is often more difficult to find an analytical solution or even a numerical one. This book has successfully handled this challenging job with the latest techniques. In addition, the findings of the simulation are logically realistic and meet the standard of sufficient scientific value.

Technology: general issues --- Synovial fluid --- coating --- shear-thinning and -thickening models --- mass transport --- asymmetric channel --- analytical solution --- thin film --- spin coating --- rotating disk --- nanoparticles --- Newtonian fluids --- coatings --- curved stretched surface --- nanoliquid --- nonlinear thermal radiation --- entropy generation --- Reiner-Phillipoff fluid --- time-dependent --- thermal radiation --- homotopy analysis method (HAM) --- thin film of micropolar fluid --- porous medium --- thermophoresis --- skin friction --- Nusselt number and Sherwood number --- variable thickness of the liquid film --- HAM --- optical fiber coating --- double-layer coating --- viscoelastic PTT fluid --- analytic and numerical simulations --- thin film casson nanofluid --- SWCNTs and MWCNTs --- stretching cylinder --- MHD --- unsteady flow and heat transfer --- nanofluid --- Blasius–Rayleigh–Stokes variable --- dual solutions --- numerical solution --- correlation expressions --- Casson fluid --- condensation film --- heat generation/consumption --- thin liquid film flow --- carbon nanotubes --- Cattaneo-Christov heat flux --- variable heat source/sink --- heated bi-phase flow --- couple stress fluid --- lubrication effects --- slippery walls --- magnetohydrodynamics --- Darcy-Forchheimer nanofluid --- nonlinear extending disc --- variable thin layer --- HAM and numerical method --- peristaltic flow --- an endoscope --- variable viscosity --- Adomian solutions --- different wave forms --- pseudo-similarity variable --- micropolar nanofluid --- darcy forchheimer model --- MHD flow --- triple solution --- stability analysis --- APCM --- Caputo derivative --- unsteady flow --- shrinking surface --- Williamson model --- peristaltic pumping --- convective boundary conditions --- analytic solutions --- second order slip --- double stratification --- Cattaneo–Christov heat flux --- variable thermal conductivity --- Williamson nanofluid --- velocity second slip --- wave forms --- exact solutions --- magnetic field --- heat and mass transfer --- Hall current --- homogeneous–heterogeneous reactions --- viscoelastic fluids --- heterogeneous–homogeneous reactions --- mixed convective flow --- binary chemical reaction --- arrhenius activation energy --- gas-liquid coatings --- bubbles --- two-fluid model --- phase distribution --- HPM --- double diffusion --- curved channel --- compliant walls --- analytical solutions --- third grade fluid model --- hybrid nanofluid --- induced magnetic field --- mixed convection --- heat generation --- peristalsis --- cilia beating --- Non-Newtonian --- Bejan number --- Jeffrey fluid model --- eccentric annuli --- droplet impact modelling --- impedance analysis --- rain erosion --- ultrasound measurements --- viscoelastic modelling --- wind turbine blades --- computational modelling --- rain erosion testing --- viscoelastic characterization --- development and characterization of coatings --- applications of thin films --- nanostructured materials --- surfaces and interfaces --- applications of multiphase fluids --- mathematical modeling on biological applications --- electronics --- magnetics and magneto-optics

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Over the past four decades, there has been increased attention given to the research of fluid mechanics due to its wide application in industry and phycology. Major advances in the modeling of key topics such Newtonian and non-Newtonian fluids and thin film flows have been made and finally published in the Special Issue of coatings. This is an attempt to edit the Special Issue into a book. Although this book is not a formal textbook, it will definitely be useful for university teachers, research students, industrial researchers and in overcoming the difficulties occurring in the said topic, while dealing with the nonlinear governing equations. For such types of equations, it is often more difficult to find an analytical solution or even a numerical one. This book has successfully handled this challenging job with the latest techniques. In addition, the findings of the simulation are logically realistic and meet the standard of sufficient scientific value.

Synovial fluid --- coating --- shear-thinning and -thickening models --- mass transport --- asymmetric channel --- analytical solution --- thin film --- spin coating --- rotating disk --- nanoparticles --- Newtonian fluids --- coatings --- curved stretched surface --- nanoliquid --- nonlinear thermal radiation --- entropy generation --- Reiner-Phillipoff fluid --- time-dependent --- thermal radiation --- homotopy analysis method (HAM) --- thin film of micropolar fluid --- porous medium --- thermophoresis --- skin friction --- Nusselt number and Sherwood number --- variable thickness of the liquid film --- HAM --- optical fiber coating --- double-layer coating --- viscoelastic PTT fluid --- analytic and numerical simulations --- thin film casson nanofluid --- SWCNTs and MWCNTs --- stretching cylinder --- MHD --- unsteady flow and heat transfer --- nanofluid --- Blasius–Rayleigh–Stokes variable --- dual solutions --- numerical solution --- correlation expressions --- Casson fluid --- condensation film --- heat generation/consumption --- thin liquid film flow --- carbon nanotubes --- Cattaneo-Christov heat flux --- variable heat source/sink --- heated bi-phase flow --- couple stress fluid --- lubrication effects --- slippery walls --- magnetohydrodynamics --- Darcy-Forchheimer nanofluid --- nonlinear extending disc --- variable thin layer --- HAM and numerical method --- peristaltic flow --- an endoscope --- variable viscosity --- Adomian solutions --- different wave forms --- pseudo-similarity variable --- micropolar nanofluid --- darcy forchheimer model --- MHD flow --- triple solution --- stability analysis --- APCM --- Caputo derivative --- unsteady flow --- shrinking surface --- Williamson model --- peristaltic pumping --- convective boundary conditions --- analytic solutions --- second order slip --- double stratification --- Cattaneo–Christov heat flux --- variable thermal conductivity --- Williamson nanofluid --- velocity second slip --- wave forms --- exact solutions --- magnetic field --- heat and mass transfer --- Hall current --- homogeneous–heterogeneous reactions --- viscoelastic fluids --- heterogeneous–homogeneous reactions --- mixed convective flow --- binary chemical reaction --- arrhenius activation energy --- gas-liquid coatings --- bubbles --- two-fluid model --- phase distribution --- HPM --- double diffusion --- curved channel --- compliant walls --- analytical solutions --- third grade fluid model --- hybrid nanofluid --- induced magnetic field --- mixed convection --- heat generation --- peristalsis --- cilia beating --- Non-Newtonian --- Bejan number --- Jeffrey fluid model --- eccentric annuli --- droplet impact modelling --- impedance analysis --- rain erosion --- ultrasound measurements --- viscoelastic modelling --- wind turbine blades --- computational modelling --- rain erosion testing --- viscoelastic characterization --- development and characterization of coatings --- applications of thin films --- nanostructured materials --- surfaces and interfaces --- applications of multiphase fluids --- mathematical modeling on biological applications --- electronics --- magnetics and magneto-optics