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The study of oscillatory phenomena is an important part of the theory of differential equations. Oscillations naturally occur in virtually every area of applied science including, e.g., mechanics, electrical, radio engineering, and vibrotechnics. This Special Issue includes 19 high-quality papers with original research results in theoretical research, and recent progress in the study of applied problems in science and technology. This Special Issue brought together mathematicians with physicists, engineers, as well as other scientists. Topics covered in this issue: Oscillation theory; Differential/difference equations; Partial differential equations; Dynamical systems; Fractional calculus; Delays; Mathematical modeling and oscillations.

Information technology industries --- odd-order differential equations --- Kneser solutions --- oscillatory solutions --- deviating argument --- fourth order --- differential equation --- oscillation --- advanced differential equations --- p-Laplacian equations --- comparison theorem --- oscillation criteria --- thrid-order --- delay differential equations --- oscillations --- Riccati transformations --- fourth-order delay equations --- differential operator --- unit disk --- univalent function --- analytic function --- subordination --- q-calculus --- fractional calculus --- fractional differential equation --- q-differential equation --- second order --- neutral differential equation --- (1/G′)-expansion method --- the Zhiber-Shabat equation --- (G′/G,1/G)-expansion method --- traveling wave solutions --- exact solutions --- Adomian decomposition method --- Caputo operator --- Natural transform --- Fornberg–Whitham equations --- generalized proportional fractional operator --- nonoscillatory behavior --- damping and forcing terms --- Volterra integral equations --- operational matrix of integration --- multi-wavelets --- time scales --- functional dynamic equations --- highly oscillatory integral --- Chebyshev polynomial --- nearly singular --- Levin quadrature rule --- adaptive mesh refinement --- la Cierva’s autogiro --- la Cierva’s equation --- stability --- differential equation with periodic coefficients --- interpolating scaling functions --- hyperbolic equation --- Galerkin method --- higher-order --- neutral delay --- center of mass --- conformal metric --- geodesic --- hyperbolic lever law --- non-canonical differential equations --- second-order --- mixed type --- odd-order differential equations --- Kneser solutions --- oscillatory solutions --- deviating argument --- fourth order --- differential equation --- oscillation --- advanced differential equations --- p-Laplacian equations --- comparison theorem --- oscillation criteria --- thrid-order --- delay differential equations --- oscillations --- Riccati transformations --- fourth-order delay equations --- differential operator --- unit disk --- univalent function --- analytic function --- subordination --- q-calculus --- fractional calculus --- fractional differential equation --- q-differential equation --- second order --- neutral differential equation --- (1/G′)-expansion method --- the Zhiber-Shabat equation --- (G′/G,1/G)-expansion method --- traveling wave solutions --- exact solutions --- Adomian decomposition method --- Caputo operator --- Natural transform --- Fornberg–Whitham equations --- generalized proportional fractional operator --- nonoscillatory behavior --- damping and forcing terms --- Volterra integral equations --- operational matrix of integration --- multi-wavelets --- time scales --- functional dynamic equations --- highly oscillatory integral --- Chebyshev polynomial --- nearly singular --- Levin quadrature rule --- adaptive mesh refinement --- la Cierva’s autogiro --- la Cierva’s equation --- stability --- differential equation with periodic coefficients --- interpolating scaling functions --- hyperbolic equation --- Galerkin method --- higher-order --- neutral delay --- center of mass --- conformal metric --- geodesic --- hyperbolic lever law --- non-canonical differential equations --- second-order --- mixed type

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

The study of oscillatory phenomena is an important part of the theory of differential equations. Oscillations naturally occur in virtually every area of applied science including, e.g., mechanics, electrical, radio engineering, and vibrotechnics. This Special Issue includes 19 high-quality papers with original research results in theoretical research, and recent progress in the study of applied problems in science and technology. This Special Issue brought together mathematicians with physicists, engineers, as well as other scientists. Topics covered in this issue: Oscillation theory; Differential/difference equations; Partial differential equations; Dynamical systems; Fractional calculus; Delays; Mathematical modeling and oscillations.

odd-order differential equations --- Kneser solutions --- oscillatory solutions --- deviating argument --- fourth order --- differential equation --- oscillation --- advanced differential equations --- p-Laplacian equations --- comparison theorem --- oscillation criteria --- thrid-order --- delay differential equations --- oscillations --- Riccati transformations --- fourth-order delay equations --- differential operator --- unit disk --- univalent function --- analytic function --- subordination --- q-calculus --- fractional calculus --- fractional differential equation --- q-differential equation --- second order --- neutral differential equation --- (1/G′)-expansion method --- the Zhiber-Shabat equation --- (G′/G,1/G)-expansion method --- traveling wave solutions --- exact solutions --- Adomian decomposition method --- Caputo operator --- Natural transform --- Fornberg–Whitham equations --- generalized proportional fractional operator --- nonoscillatory behavior --- damping and forcing terms --- Volterra integral equations --- operational matrix of integration --- multi-wavelets --- time scales --- functional dynamic equations --- highly oscillatory integral --- Chebyshev polynomial --- nearly singular --- Levin quadrature rule --- adaptive mesh refinement --- la Cierva’s autogiro --- la Cierva’s equation --- stability --- differential equation with periodic coefficients --- interpolating scaling functions --- hyperbolic equation --- Galerkin method --- higher-order --- neutral delay --- center of mass --- conformal metric --- geodesic --- hyperbolic lever law --- non-canonical differential equations --- second-order --- mixed type

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There are many applications of mathematical physics in several fields of basic science and engineering. Thus, we have tried to provide the Special Issue “Modern Problems of Mathematical Physics and Their Applications” to cover the new advances of mathematical physics and its applications. In this Special Issue, we have focused on some important and challenging topics, such as integral equations, ill-posed problems, ordinary differential equations, partial differential equations, system of equations, fractional problems, linear and nonlinear problems, fuzzy problems, numerical methods, analytical methods, semi-analytical methods, convergence analysis, error analysis and mathematical models. In response to our invitation, we received 31 papers from more than 17 countries (Russia, Uzbekistan, China, USA, Kuwait, Bosnia and Herzegovina, Thailand, Pakistan, Turkey, Nigeria, Jordan, Romania, India, Iran, Argentina, Israel, Canada, etc.), of which 19 were published and 12 rejected.

Research & information: general --- Mathematics & science --- cauchy problem --- regularization --- factorization --- regular solution --- fundamental solution --- road section --- IMF SWARA --- traffic safety --- fuzzy MARCOS --- DEA --- ordinary differential equations --- analytical methods --- mathematical models --- Riccati equation --- radial Schrödinger equation --- transformations --- hyper-singular integrals --- Navier-Stokes problem --- product user experience --- enterprise network public opinion --- identification of high-risk users --- random forest algorithm --- user portrait --- controlled second-order Lagrangian --- Euler-Lagrange equations --- isoperimetric constraints --- curvilinear integral --- differential 1-form --- partition functions --- analytical extensions --- guelfand's and gradshteyn's --- classical gravity --- internal waves in rotating ocean --- fractional derivative --- q-Homotopy analysis transform technique --- fixed point theorem --- minimal sensitivity --- optimization --- power transform --- critical index --- secant method --- generalized secant method --- complex roots --- cressman method --- EICM --- ENSO --- SSTA --- immune system --- virus-infected cell --- effector cell --- autoimmune disease --- time-delay virus-immune model --- differential equations --- differential operators --- non-local boundary value problems --- general conditions --- integral conditions --- multipoint conditions --- composition of operators --- pseudo-differential equation --- conjugation problem --- wave factorization --- solvability condition --- measure of noncompactness --- random effect --- random operator --- Mönch's fixed point theorem --- multi-term fractional differential equation --- Carathéodory condition --- resolvent family theory --- multi-dimensional public opinion --- topic derivation --- complex network dynamics model --- online comments --- hot events --- fluid --- flows --- dynamic --- structure --- axiomatics --- fundamental equations --- dissipation --- complete solution --- ligaments --- waves --- vortices --- plate --- wake --- drop --- impact --- boundary element method --- barrier options --- multi-asset options --- basket options --- spread options --- thrid-order differential equations --- delay --- oscillation criteria --- cauchy problem --- regularization --- factorization --- regular solution --- fundamental solution --- road section --- IMF SWARA --- traffic safety --- fuzzy MARCOS --- DEA --- ordinary differential equations --- analytical methods --- mathematical models --- Riccati equation --- radial Schrödinger equation --- transformations --- hyper-singular integrals --- Navier-Stokes problem --- product user experience --- enterprise network public opinion --- identification of high-risk users --- random forest algorithm --- user portrait --- controlled second-order Lagrangian --- Euler-Lagrange equations --- isoperimetric constraints --- curvilinear integral --- differential 1-form --- partition functions --- analytical extensions --- guelfand's and gradshteyn's --- classical gravity --- internal waves in rotating ocean --- fractional derivative --- q-Homotopy analysis transform technique --- fixed point theorem --- minimal sensitivity --- optimization --- power transform --- critical index --- secant method --- generalized secant method --- complex roots --- cressman method --- EICM --- ENSO --- SSTA --- immune system --- virus-infected cell --- effector cell --- autoimmune disease --- time-delay virus-immune model --- differential equations --- differential operators --- non-local boundary value problems --- general conditions --- integral conditions --- multipoint conditions --- composition of operators --- pseudo-differential equation --- conjugation problem --- wave factorization --- solvability condition --- measure of noncompactness --- random effect --- random operator --- Mönch's fixed point theorem --- multi-term fractional differential equation --- Carathéodory condition --- resolvent family theory --- multi-dimensional public opinion --- topic derivation --- complex network dynamics model --- online comments --- hot events --- fluid --- flows --- dynamic --- structure --- axiomatics --- fundamental equations --- dissipation --- complete solution --- ligaments --- waves --- vortices --- plate --- wake --- drop --- impact --- boundary element method --- barrier options --- multi-asset options --- basket options --- spread options --- thrid-order differential equations --- delay --- oscillation criteria