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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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In the last three decades, fractional calculus has broken into the field of mathematical analysis, both at the theoretical level and at the level of its applications. In essence, the fractional calculus theory is a mathematical analysis tool applied to the study of integrals and derivatives of arbitrary order, which unifies and generalizes the classical notions of differentiation and integration. These fractional and derivative integrals, which until not many years ago had been used in purely mathematical contexts, have been revealed as instruments with great potential to model problems in various scientific fields, such as: fluid mechanics, viscoelasticity, physics, biology, chemistry, dynamical systems, signal processing or entropy theory. Since the differential and integral operators of fractional order are nonlinear operators, fractional calculus theory provides a tool for modeling physical processes, which in many cases is more useful than classical formulations. This is why the application of fractional calculus theory has become a focus of international academic research. This Special Issue "Applied Mathematics and Fractional Calculus" has published excellent research studies in the field of applied mathematics and fractional calculus, authored by many well-known mathematicians and scientists from diverse countries worldwide such as China, USA, Canada, Germany, Mexico, Spain, Poland, Portugal, Iran, Tunisia, South Africa, Albania, Thailand, Iraq, Egypt, Italy, India, Russia, Pakistan, Taiwan, Korea, Turkey, and Saudi Arabia.

Research & information: general --- Mathematics & science --- condensing function --- approximate endpoint criterion --- quantum integro-difference BVP --- existence --- fractional Kadomtsev-Petviashvili system --- lie group analysis --- power series solutions --- convergence analysis --- conservation laws --- symmetry --- weighted fractional operators --- convex functions --- HHF type inequality --- fractional calculus --- Euler–Lagrange equation --- natural boundary conditions --- time delay --- MHD equations --- weak solution --- regularity criteria --- anisotropic Lorentz space --- Sonine kernel --- general fractional derivative of arbitrary order --- general fractional integral of arbitrary order --- first fundamental theorem of fractional calculus --- second fundamental theorem of fractional calculus --- ρ-Laplace variational iteration method --- ρ-Laplace decomposition method --- partial differential equation --- caputo operator --- fractional Fornberg–Whitham equation (FWE) --- Riemann–Liouville fractional difference operator --- boundary value problem --- discrete fractional calculus --- existence and uniqueness --- Ulam stability --- elastic beam problem --- tempered fractional derivative --- one-sided tempered fractional derivative --- bilateral tempered fractional derivative --- tempered riesz potential --- collocation method --- hermite cubic spline --- fractional burgers equation --- fractional differential equation --- fractional Dzhrbashyan–Nersesyan derivative --- degenerate evolution equation --- initial value problem --- initial boundary value problem --- partial Riemann–Liouville fractional integral --- Babenko’s approach --- Banach fixed point theorem --- Mittag–Leffler function --- gamma function --- nabla fractional difference --- separated boundary conditions --- Green’s function --- existence of solutions --- Caputo q-derivative --- singular sum fractional q-differential --- fixed point --- equations --- Riemann–Liouville q-integral --- Shehu transform --- Caputo fractional derivative --- Shehu decomposition method --- new iterative transform method --- fractional KdV equation --- approximate solutions --- Riemann–Liouville derivative --- concave operator --- fixed point theorem --- Gelfand problem --- order cone --- integral transform --- Atangana–Baleanu fractional derivative --- Aboodh transform iterative method --- φ-Hilfer fractional system with impulses --- semigroup theory --- nonlocal conditions --- optimal controls --- fractional derivatives --- fractional Prabhakar derivatives --- fractional differential equations --- fractional Sturm–Liouville problems --- eigenfunctions and eigenvalues --- Fredholm–Volterra integral Equations --- fractional derivative --- Bessel polynomials --- Caputo derivative --- collocation points --- Caputo–Fabrizio and Atangana-Baleanu operators --- time-fractional Kaup–Kupershmidt equation --- natural transform --- Adomian decomposition method --- condensing function --- approximate endpoint criterion --- quantum integro-difference BVP --- existence --- fractional Kadomtsev-Petviashvili system --- lie group analysis --- power series solutions --- convergence analysis --- conservation laws --- symmetry --- weighted fractional operators --- convex functions --- HHF type inequality --- fractional calculus --- Euler–Lagrange equation --- natural boundary conditions --- time delay --- MHD equations --- weak solution --- regularity criteria --- anisotropic Lorentz space --- Sonine kernel --- general fractional derivative of arbitrary order --- general fractional integral of arbitrary order --- first fundamental theorem of fractional calculus --- second fundamental theorem of fractional calculus --- ρ-Laplace variational iteration method --- ρ-Laplace decomposition method --- partial differential equation --- caputo operator --- fractional Fornberg–Whitham equation (FWE) --- Riemann–Liouville fractional difference operator --- boundary value problem --- discrete fractional calculus --- existence and uniqueness --- Ulam stability --- elastic beam problem --- tempered fractional derivative --- one-sided tempered fractional derivative --- bilateral tempered fractional derivative --- tempered riesz potential --- collocation method --- hermite cubic spline --- fractional burgers equation --- fractional differential equation --- fractional Dzhrbashyan–Nersesyan derivative --- degenerate evolution equation --- initial value problem --- initial boundary value problem --- partial Riemann–Liouville fractional integral --- Babenko’s approach --- Banach fixed point theorem --- Mittag–Leffler function --- gamma function --- nabla fractional difference --- separated boundary conditions --- Green’s function --- existence of solutions --- Caputo q-derivative --- singular sum fractional q-differential --- fixed point --- equations --- Riemann–Liouville q-integral --- Shehu transform --- Caputo fractional derivative --- Shehu decomposition method --- new iterative transform method --- fractional KdV equation --- approximate solutions --- Riemann–Liouville derivative --- concave operator --- fixed point theorem --- Gelfand problem --- order cone --- integral transform --- Atangana–Baleanu fractional derivative --- Aboodh transform iterative method --- φ-Hilfer fractional system with impulses --- semigroup theory --- nonlocal conditions --- optimal controls --- fractional derivatives --- fractional Prabhakar derivatives --- fractional differential equations --- fractional Sturm–Liouville problems --- eigenfunctions and eigenvalues --- Fredholm–Volterra integral Equations --- fractional derivative --- Bessel polynomials --- Caputo derivative --- collocation points --- Caputo–Fabrizio and Atangana-Baleanu operators --- time-fractional Kaup–Kupershmidt equation --- natural transform --- Adomian decomposition method

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In the last three decades, fractional calculus has broken into the field of mathematical analysis, both at the theoretical level and at the level of its applications. In essence, the fractional calculus theory is a mathematical analysis tool applied to the study of integrals and derivatives of arbitrary order, which unifies and generalizes the classical notions of differentiation and integration. These fractional and derivative integrals, which until not many years ago had been used in purely mathematical contexts, have been revealed as instruments with great potential to model problems in various scientific fields, such as: fluid mechanics, viscoelasticity, physics, biology, chemistry, dynamical systems, signal processing or entropy theory. Since the differential and integral operators of fractional order are nonlinear operators, fractional calculus theory provides a tool for modeling physical processes, which in many cases is more useful than classical formulations. This is why the application of fractional calculus theory has become a focus of international academic research. This Special Issue "Applied Mathematics and Fractional Calculus" has published excellent research studies in the field of applied mathematics and fractional calculus, authored by many well-known mathematicians and scientists from diverse countries worldwide such as China, USA, Canada, Germany, Mexico, Spain, Poland, Portugal, Iran, Tunisia, South Africa, Albania, Thailand, Iraq, Egypt, Italy, India, Russia, Pakistan, Taiwan, Korea, Turkey, and Saudi Arabia.

condensing function --- approximate endpoint criterion --- quantum integro-difference BVP --- existence --- fractional Kadomtsev-Petviashvili system --- lie group analysis --- power series solutions --- convergence analysis --- conservation laws --- symmetry --- weighted fractional operators --- convex functions --- HHF type inequality --- fractional calculus --- Euler–Lagrange equation --- natural boundary conditions --- time delay --- MHD equations --- weak solution --- regularity criteria --- anisotropic Lorentz space --- Sonine kernel --- general fractional derivative of arbitrary order --- general fractional integral of arbitrary order --- first fundamental theorem of fractional calculus --- second fundamental theorem of fractional calculus --- ρ-Laplace variational iteration method --- ρ-Laplace decomposition method --- partial differential equation --- caputo operator --- fractional Fornberg–Whitham equation (FWE) --- Riemann–Liouville fractional difference operator --- boundary value problem --- discrete fractional calculus --- existence and uniqueness --- Ulam stability --- elastic beam problem --- tempered fractional derivative --- one-sided tempered fractional derivative --- bilateral tempered fractional derivative --- tempered riesz potential --- collocation method --- hermite cubic spline --- fractional burgers equation --- fractional differential equation --- fractional Dzhrbashyan–Nersesyan derivative --- degenerate evolution equation --- initial value problem --- initial boundary value problem --- partial Riemann–Liouville fractional integral --- Babenko’s approach --- Banach fixed point theorem --- Mittag–Leffler function --- gamma function --- nabla fractional difference --- separated boundary conditions --- Green’s function --- existence of solutions --- Caputo q-derivative --- singular sum fractional q-differential --- fixed point --- equations --- Riemann–Liouville q-integral --- Shehu transform --- Caputo fractional derivative --- Shehu decomposition method --- new iterative transform method --- fractional KdV equation --- approximate solutions --- Riemann–Liouville derivative --- concave operator --- fixed point theorem --- Gelfand problem --- order cone --- integral transform --- Atangana–Baleanu fractional derivative --- Aboodh transform iterative method --- φ-Hilfer fractional system with impulses --- semigroup theory --- nonlocal conditions --- optimal controls --- fractional derivatives --- fractional Prabhakar derivatives --- fractional differential equations --- fractional Sturm–Liouville problems --- eigenfunctions and eigenvalues --- Fredholm–Volterra integral Equations --- fractional derivative --- Bessel polynomials --- Caputo derivative --- collocation points --- Caputo–Fabrizio and Atangana-Baleanu operators --- time-fractional Kaup–Kupershmidt equation --- natural transform --- Adomian decomposition method