Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 12/2018, Volume 117, pp. 117 - 124

In this article, by popularization of the reproducing kernel Hilbert space method in the sense of the Atangana–Baleanu fractional operator; set of first-order...

Atangana–Baleanu fractional operator | Integrodifferential equations | Fredholm operator | Reproducing kernel Hilbert space method | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | TURNING-POINT PROBLEMS | ALGORITHM | REPRODUCING KERNEL-METHOD | PHYSICS, MATHEMATICAL | DERIVATIVES | Atangana-Baleanu fractional operator

Atangana–Baleanu fractional operator | Integrodifferential equations | Fredholm operator | Reproducing kernel Hilbert space method | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | TURNING-POINT PROBLEMS | ALGORITHM | REPRODUCING KERNEL-METHOD | PHYSICS, MATHEMATICAL | DERIVATIVES | Atangana-Baleanu fractional operator

Journal Article

Annals of Physics, ISSN 0003-4916, 02/2008, Volume 323, Issue 2, pp. 500 - 526

We show that the technique of integration within normal ordering of operators [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480–494] applied to...

Similarity transform and Weyl ordering covariance | Weyl ordering | Weyl ordered Wigner operator | Entangled state representation | Wigner transform | The integration for ket–bra operators | The IWWOP technique | The integration for ket-bra operators | the integration for ket-bra operators | PHASE-SPACE | PHYSICS, MULTIDISCIPLINARY | FRACTIONAL FOURIER-TRANSFORM | WIGNER-DISTRIBUTION | MODE | the IWWOP technique | entangled state representation | VIRTUE | IWOP TECHNIQUE | SQUEEZED STATES | similarity transform and Weyl ordering covariance | OPTICS | COHERENT-STATE REPRESENTATION | SYMPLECTIC TRANSFORMATIONS | Integrated approach | Mathematics | Statistical analysis | Physics | Quantum theory | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | STATISTICS | SIGNALS | PROJECTION OPERATORS | QUANTUM ENTANGLEMENT | QUANTUM MECHANICS | TRANSFORMATIONS

Similarity transform and Weyl ordering covariance | Weyl ordering | Weyl ordered Wigner operator | Entangled state representation | Wigner transform | The integration for ket–bra operators | The IWWOP technique | The integration for ket-bra operators | the integration for ket-bra operators | PHASE-SPACE | PHYSICS, MULTIDISCIPLINARY | FRACTIONAL FOURIER-TRANSFORM | WIGNER-DISTRIBUTION | MODE | the IWWOP technique | entangled state representation | VIRTUE | IWOP TECHNIQUE | SQUEEZED STATES | similarity transform and Weyl ordering covariance | OPTICS | COHERENT-STATE REPRESENTATION | SYMPLECTIC TRANSFORMATIONS | Integrated approach | Mathematics | Statistical analysis | Physics | Quantum theory | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | STATISTICS | SIGNALS | PROJECTION OPERATORS | QUANTUM ENTANGLEMENT | QUANTUM MECHANICS | TRANSFORMATIONS

Journal Article

3.
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Dilation operators and integral operators on amalgam space $$(L_{p},l_{q})$$ ( L p , l q )

Ricerche di Matematica, ISSN 0035-5038, 12/2019, Volume 68, Issue 2, pp. 661 - 677

This paper establishes the Hardy–Littlewood–Pólya inequalities, the Hardy inequalities and the Hilbert inequalities on amalgam spaces. Moreover, it also gives...

Integral operator | 26D10 | Probability Theory and Stochastic Processes | Hardy inequality | Mathematics | Amalgam spaces | Mellin convolution | Geometry | 42B35 | Algebra | 44A05 | Analysis | Numerical Analysis | Hilbert inequality | 46E30 | Mathematics, general | Hausdorff operator | 26D15 | Hadamard fractional integral

Integral operator | 26D10 | Probability Theory and Stochastic Processes | Hardy inequality | Mathematics | Amalgam spaces | Mellin convolution | Geometry | 42B35 | Algebra | 44A05 | Analysis | Numerical Analysis | Hilbert inequality | 46E30 | Mathematics, general | Hausdorff operator | 26D15 | Hadamard fractional integral

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 06/2018, Volume 59, pp. 608 - 611

This short note analyses the Caputo–Fabrizio operator. It is verified that it does not fit the usual concepts neither for fractional nor for integer...

Caputo-Fabrizio operator | Fractional derivative | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | Electrical engineering | Analysis

Caputo-Fabrizio operator | Fractional derivative | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | Electrical engineering | Analysis

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 02/2016, Volume 270, Issue 4, pp. 1416 - 1478

We consider a class of non-uniformly nonlinear elliptic equations whose model is given by where and , and establish the related nonlinear Calderón–Zygmund...

Degenerate operators | Non-uniform ellipticity | Regularity | Calderón–Zygmund estimates | Calderón-Zygmund estimates | EQUATIONS | Calderon-Zygmund estimates | Q-GROWTH | GRADIENT | MINIMIZERS | MATHEMATICS | INTEGRAL FUNCTIONALS | PARABOLIC-SYSTEMS | VARIATIONAL-PROBLEMS | WEAK SOLUTIONS | FRACTIONAL SOBOLEV SPACES

Degenerate operators | Non-uniform ellipticity | Regularity | Calderón–Zygmund estimates | Calderón-Zygmund estimates | EQUATIONS | Calderon-Zygmund estimates | Q-GROWTH | GRADIENT | MINIMIZERS | MATHEMATICS | INTEGRAL FUNCTIONALS | PARABOLIC-SYSTEMS | VARIATIONAL-PROBLEMS | WEAK SOLUTIONS | FRACTIONAL SOBOLEV SPACES

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 10/2013, Volume 66, Issue 7, pp. 1245 - 1260

We analyze a nonlocal diffusion operator having as special cases the fractional Laplacian and fractional differential operators that arise in several...

Nonlocal vector calculus | Fractional Laplacian | Finite element methods | Nonlocal diffusion | Fractional Sobolev spaces | Nonlocal operators | MATHEMATICS, APPLIED | TRANSPORT | APPROXIMATION | EQUATIONS | DYNAMICS

Nonlocal vector calculus | Fractional Laplacian | Finite element methods | Nonlocal diffusion | Fractional Sobolev spaces | Nonlocal operators | MATHEMATICS, APPLIED | TRANSPORT | APPROXIMATION | EQUATIONS | DYNAMICS

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 11/2011, Volume 71, Issue 3, pp. 327 - 355

In this paper the authors study the boundedness for a large class of sublinear operators $${T_{\alpha}, \alpha \in [0,n)}$$ generated by Calderón–Zygmund...

Littlewood–Paley operator | BMO | Marcinkiewicz operator | Calderón–Zygmund operator | generalized Morrey space | Mathematics | commutator | Primary 42B20 | 42B35 | 42B25 | Riesz potential operator | Analysis | fractional maximal operator | Sublinear operator | Bochner–Riesz operator | Bochner-Riesz operator | Calderón-Zygmund operator | Littlewood-Paley operator | SUFFICIENT CONDITIONS | EQUATIONS | INTEGRALS | MATHEMATICS | Calderon-Zygmund operator | COEFFICIENTS | SCHRODINGER-OPERATORS | RIESZ-POTENTIALS

Littlewood–Paley operator | BMO | Marcinkiewicz operator | Calderón–Zygmund operator | generalized Morrey space | Mathematics | commutator | Primary 42B20 | 42B35 | 42B25 | Riesz potential operator | Analysis | fractional maximal operator | Sublinear operator | Bochner–Riesz operator | Bochner-Riesz operator | Calderón-Zygmund operator | Littlewood-Paley operator | SUFFICIENT CONDITIONS | EQUATIONS | INTEGRALS | MATHEMATICS | Calderon-Zygmund operator | COEFFICIENTS | SCHRODINGER-OPERATORS | RIESZ-POTENTIALS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 01/2014, Volume 94, pp. 156 - 170

In this paper we show the existence of non-negative solutions for a Kirchhoff type problem driven by a nonlocal integrodifferential operator, that is where is...

Fractional Laplacian | Vibrating string | Kirchhoff equation | Fractional | Laplacian | MATHEMATICS, APPLIED | MINIMAL-SURFACES | MULTIPLICITY | EQUATIONS | MATHEMATICS | ELLIPTIC PROBLEMS | R-N | CRITICAL GROWTH | DYNAMIC BOUNDARY-CONDITIONS | SYSTEMS | Nonlinearity

Fractional Laplacian | Vibrating string | Kirchhoff equation | Fractional | Laplacian | MATHEMATICS, APPLIED | MINIMAL-SURFACES | MULTIPLICITY | EQUATIONS | MATHEMATICS | ELLIPTIC PROBLEMS | R-N | CRITICAL GROWTH | DYNAMIC BOUNDARY-CONDITIONS | SYSTEMS | Nonlinearity

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2017, Volume 448, Issue 2, pp. 1633 - 1650

In this work, following a new approach of Baliarsingh (2016) , we introduce the concepts of statistically weighted -summability, weighted -statistical...

The difference operator [formula omitted] | Korovkin type approximations for functions of two variables | [formula omitted]-analogue of Bernstein–Schurer operator | Weighted statistical convergence and statistical summability | The rate of convergence | (p,q)-analogue of Bernstein–Schurer operator | The difference operator Δ | FRACTIONAL ORDER | MATHEMATICS | MATHEMATICS, APPLIED | SEQUENCE-SPACES | KOROVKIN | (p, q)-analogue of Bernstein-Schurer operator | The difference operator Delta(alpha,beta,gamma)(h,p,q)

The difference operator [formula omitted] | Korovkin type approximations for functions of two variables | [formula omitted]-analogue of Bernstein–Schurer operator | Weighted statistical convergence and statistical summability | The rate of convergence | (p,q)-analogue of Bernstein–Schurer operator | The difference operator Δ | FRACTIONAL ORDER | MATHEMATICS | MATHEMATICS, APPLIED | SEQUENCE-SPACES | KOROVKIN | (p, q)-analogue of Bernstein-Schurer operator | The difference operator Delta(alpha,beta,gamma)(h,p,q)

Journal Article

Russian Mathematical Surveys, ISSN 0036-0279, 2016, Volume 71, Issue 4, pp. 605 - 702

The goal of this survey is a comprehensive study of operator Lipschitz functions. A continuous function f on the real line R is said to be operator Lipschitz...

Normal operators | Divided differences | Operator differentiable functions | Operator Lipschitz functions | Schur multipliers | Besov classes | Double operator integrals | Linear-fractional transformations | Carleson measures | Functions of operators | Self-adjoint operators | SMOOTH FUNCTIONS | normal operators | self-adjoint operators | double operator integrals | operator differentiable functions | divided differences | INTEGRALS | MATHEMATICS | operator Lipschitz functions | linear-fractional transformations | functions of operators | Functions (mathematics) | Operators (mathematics) | Operators | Multipliers | Planes | Integrals | Mathematical analysis | Commutators

Normal operators | Divided differences | Operator differentiable functions | Operator Lipschitz functions | Schur multipliers | Besov classes | Double operator integrals | Linear-fractional transformations | Carleson measures | Functions of operators | Self-adjoint operators | SMOOTH FUNCTIONS | normal operators | self-adjoint operators | double operator integrals | operator differentiable functions | divided differences | INTEGRALS | MATHEMATICS | operator Lipschitz functions | linear-fractional transformations | functions of operators | Functions (mathematics) | Operators (mathematics) | Operators | Multipliers | Planes | Integrals | Mathematical analysis | Commutators

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2020, Volume 482, Issue 1, p. 123523

Let be a Schrödinger operator on the Heisenberg group , where is the sublaplacian on and the nonnegative potential belongs to the reverse Hölder class with ....

Reverse Hölder class | Heisenberg group | Morrey spaces | Fractional integral operators | Schrödinger operator | Adams inequality | MATHEMATICS | MATHEMATICS, APPLIED | COMPLEX | WEIGHTED INEQUALITIES | EQUATIONS | Schrodinger operator | COMMUTATORS | Reverse Holder class

Reverse Hölder class | Heisenberg group | Morrey spaces | Fractional integral operators | Schrödinger operator | Adams inequality | MATHEMATICS | MATHEMATICS, APPLIED | COMPLEX | WEIGHTED INEQUALITIES | EQUATIONS | Schrodinger operator | COMMUTATORS | Reverse Holder class

Journal Article

INDIANA UNIVERSITY MATHEMATICS JOURNAL, ISSN 0022-2518, 2018, Volume 67, Issue 1, pp. 293 - 327

We describe a set of conformally covariant boundary operators associated to the Paneitz operator, in the sense that they give rise to a conformally covariant...

MATHEMATICS | Poincare-Einstein manifold | CONSTANT MEAN-CURVATURE | boundary operator | Conformally covariant operator | DETERMINANTS | fractional Laplacian | MANIFOLDS | Sobolev trace inequality | SCALAR-FLAT METRICS | SOBOLEV

MATHEMATICS | Poincare-Einstein manifold | CONSTANT MEAN-CURVATURE | boundary operator | Conformally covariant operator | DETERMINANTS | fractional Laplacian | MANIFOLDS | Sobolev trace inequality | SCALAR-FLAT METRICS | SOBOLEV

Journal Article

13.
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A new operator splitting method for American options under fractional Black–Scholes models

Computers and Mathematics with Applications, ISSN 0898-1221, 04/2019, Volume 77, Issue 8, pp. 2130 - 2144

A new operator splitting method is proposed for American options under time-fractional Black–Scholes models. The fractional linear complementarity problem is...

Operator splitting | Black–Scholes | Order of convergence | American option | Linear complementarity problem | Fractional calculus | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | APPROXIMATION | Black-Scholes | DOUBLE-BARRIER OPTIONS | African Americans | Analysis | Methods | Splitting | Mathematical models | Convolution

Operator splitting | Black–Scholes | Order of convergence | American option | Linear complementarity problem | Fractional calculus | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | APPROXIMATION | Black-Scholes | DOUBLE-BARRIER OPTIONS | African Americans | Analysis | Methods | Splitting | Mathematical models | Convolution

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 09/2016, Volume 38, pp. 178 - 191

Several classes of differential and integral operators of non integer order have been proposed in the past to model systems exhibiting anomalous and hereditary...

Prabhakar function | Grünwald–Letnikov | Numerical methods | Mittag-Leffler function | Fractional calculus | Havriliak–Negami model | Havriliak-Negami model | Grünwald-Letnikov | MATHEMATICS, APPLIED | CONVOLUTION QUADRATURE | PHYSICS, FLUIDS & PLASMAS | CALCULUS | DIELECTRIC-RELAXATION | PHYSICS, MATHEMATICAL | SCHEME | LAWS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Grunwald-Letnikov | ANOMALOUS RELAXATION | FRAMEWORK | DERIVATIVES | Mechanical engineering | Analysis | Models | Electromagnetism

Prabhakar function | Grünwald–Letnikov | Numerical methods | Mittag-Leffler function | Fractional calculus | Havriliak–Negami model | Havriliak-Negami model | Grünwald-Letnikov | MATHEMATICS, APPLIED | CONVOLUTION QUADRATURE | PHYSICS, FLUIDS & PLASMAS | CALCULUS | DIELECTRIC-RELAXATION | PHYSICS, MATHEMATICAL | SCHEME | LAWS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Grunwald-Letnikov | ANOMALOUS RELAXATION | FRAMEWORK | DERIVATIVES | Mechanical engineering | Analysis | Models | Electromagnetism

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 09/2017, Volume 481, pp. 276 - 283

In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The...

Fourier transform | Laplace transform | Fractional derivative of variable-order | Anomalous diffusion | PHYSICS, MULTIDISCIPLINARY | EQUATION | Electrical engineering | Rock mechanics | Physics - Statistical Mechanics

Fourier transform | Laplace transform | Fractional derivative of variable-order | Anomalous diffusion | PHYSICS, MULTIDISCIPLINARY | EQUATION | Electrical engineering | Rock mechanics | Physics - Statistical Mechanics

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2009, Volume 211, Issue 1, pp. 198 - 210

In this paper, we introduce and investigate a fractional calculus with an integral operator which contains the following family of generalized Mittag–Leffler...

Bounded integral operators | Fractional differential equations | Caputo fractional derivative operator | Fox–Wright [formula omitted]-function | F, G and H functions | Generalized Mittag–Leffler functions | Hilfer fractional derivative operator | Laplace transformation | Lebesgue measurable functions | Riemann–Liouville fractional integral and fractional derivative operators | Fox-Wright | Riemann-Liouville fractional integral and fractional derivative operators | function | Generalized Mittag-Leffler functions | HYPERGEOMETRIC POLYNOMIALS | MATHEMATICS, APPLIED | Fox-Wright (p)Psi(q)-function | FAMILIES

Bounded integral operators | Fractional differential equations | Caputo fractional derivative operator | Fox–Wright [formula omitted]-function | F, G and H functions | Generalized Mittag–Leffler functions | Hilfer fractional derivative operator | Laplace transformation | Lebesgue measurable functions | Riemann–Liouville fractional integral and fractional derivative operators | Fox-Wright | Riemann-Liouville fractional integral and fractional derivative operators | function | Generalized Mittag-Leffler functions | HYPERGEOMETRIC POLYNOMIALS | MATHEMATICS, APPLIED | Fox-Wright (p)Psi(q)-function | FAMILIES

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 02/2017, Volume 20, Issue 1, pp. 7 - 51

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2019, Volume 474, Issue 1, pp. 94 - 115

This work studies the fractional maximal operator acting between Orlicz spaces. The necessary and sufficient conditions for the existence of optimal target and...

Fractional maximal operator | Reduction theorem | Optimality | Orlicz spaces | MATHEMATICS | MATHEMATICS, APPLIED | SOBOLEV EMBEDDINGS | INEQUALITIES | Mathematics - Functional Analysis

Fractional maximal operator | Reduction theorem | Optimality | Orlicz spaces | MATHEMATICS | MATHEMATICS, APPLIED | SOBOLEV EMBEDDINGS | INEQUALITIES | Mathematics - Functional Analysis

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 09/2018, Volume 505, pp. 688 - 706

We presented an analysis of evolutions equations generated by three fractional derivatives namely the Riemann–Liouville, Caputo–Fabrizio and the...

Non-markovian process | Semi-group principle | Markovian process | Evolution equations | Fractional derivatives | PHYSICS, MULTIDISCIPLINARY | Markov processes | Water, Underground | Organic farming | Laws, regulations and rules | Analysis

Non-markovian process | Semi-group principle | Markovian process | Evolution equations | Fractional derivatives | PHYSICS, MULTIDISCIPLINARY | Markov processes | Water, Underground | Organic farming | Laws, regulations and rules | Analysis

Journal Article