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This book includes 13 papers concerning some of the recent progress in the theory of function spaces and its applications. The involved function spaces include Morrey and weak Morrey spaces, Hardy-type spaces, John–Nirenberg spaces, Sobolev spaces, and Besov and Triebel–Lizorkin spaces on different underlying spaces, and they are applied in the study of problems ranging from harmonic analysis to potential analysis and partial differential equations, such as the boundedness of paraproducts and Calderón operators, the characterization of pointwise multipliers, estimates of anisotropic logarithmic potential, as well as certain Dirichlet problems for the Schrödinger equation.

expansive matrix --- (mixed-norm) Hardy space --- molecule --- Calderón–Zygmund operator --- real interpolation --- besov space --- meyer wavelet --- Euclidean space --- cube --- congruent cube --- BMO --- JNp --- (localized) John–Nirenberg–Campanato space --- Riesz–Morrey space --- vanishing John–Nirenberg space --- duality --- commutator --- commutators --- Riesz potential --- homogeneous group --- space of homogeneous type --- paraproduct --- T(1) theorem --- hardy space --- bilinear estimate --- Hajłasz–Sobolev space --- Hajłasz–Besov space --- Hajłasz–Triebel–Lizorkin space --- generalized smoothness --- Lebesgue point --- capacity --- pointwise multipliers --- Morrey spaces --- block spaces --- convexification --- Calderón operator --- Hardy’s inequality --- variable Lebesgue space --- local Morrey space --- local block space --- extrapolation --- anisotropy --- Hardy space --- continuous ellipsoid cover --- maximal function --- anisotropic log-potential --- optimal polynomial inequality --- annulus body --- dual log-mixed volume --- Sobolev spaces --- compact manifolds --- tensor bundles --- differential operators --- Triebel–Lizorkin space --- Hardy inequality --- uniform domain --- fractional Laplacian --- Schrödinger equation --- Morrey space --- Dirichlet problem --- metric measure space

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

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