Fractional Calculus and Applied Analysis, ISSN 1311-0454, 12/2016, Volume 19, Issue 6, pp. 1554 - 1562

Time-dependent fractional-derivative problems are considered, where is a Caputo fractional derivative of order ∈ (0, 1)∪(1, 2) and is a classical elliptic...

fractional wave equation | regularity of solution | Primary 35R11 | fractional heat equation | Secondary 35B65 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | WAVE EQUATIONS | FRACTIONAL DIFFUSION EQUATION | Wave equation | Heat equation | Analysis | Initial conditions | Regularity | Uniqueness | Mathematics - Analysis of PDEs

fractional wave equation | regularity of solution | Primary 35R11 | fractional heat equation | Secondary 35B65 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | WAVE EQUATIONS | FRACTIONAL DIFFUSION EQUATION | Wave equation | Heat equation | Analysis | Initial conditions | Regularity | Uniqueness | Mathematics - Analysis of PDEs

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 01/2020, Volume 45, Issue 1, pp. 57 - 75

We show that the fractional Laplacian on fails to satisfy the Bakry-Émery curvature-dimension inequality for all curvature bounds and all finite dimensions N >...

Gamma calculus | 60G22 (secondary) | 26D10 | Bakry-Émery curvature-dimension condition | fractional Laplacian | 35R11 (primary) | 47D07 | Curvature

Gamma calculus | 60G22 (secondary) | 26D10 | Bakry-Émery curvature-dimension condition | fractional Laplacian | 35R11 (primary) | 47D07 | Curvature

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 08/2016, Volume 19, Issue 4, pp. 806 - 831

Recently, in series of papers we have proposed different concepts of solutions of impulsive fractional differential equations (IFDE). This paper is a survey of...

fractional calculus | Primary 26A33 | noninstantaneous impulsive fractional differential equations | 35R11 | Mittag-Leffler type functions | Secondary 33E12 | 34K37 | fractional ordinary and partial differential equations | 34A08 | nonlocal impulsive fractional switched systems | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Boundary values | Solutions | Mathematical analysis | Differential equations

fractional calculus | Primary 26A33 | noninstantaneous impulsive fractional differential equations | 35R11 | Mittag-Leffler type functions | Secondary 33E12 | 34K37 | fractional ordinary and partial differential equations | 34A08 | nonlocal impulsive fractional switched systems | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Boundary values | Solutions | Mathematical analysis | Differential equations

Journal Article

Journal of the London Mathematical Society, ISSN 0024-6107, 04/2018, Volume 97, Issue 2, pp. 196 - 221

In this paper, we classify the singularities of nonnegative solutions to fractional elliptic equation 1 (−Δ)αu=up in Ω∖{0},(−Δ)αu=0 in RN∖Ω,where p>1, α∈(0,1),...

35J75 | 35B40 | 35R11 (primary) | LAPLACIAN | MATHEMATICS | LOCAL BEHAVIOR | BOUNDARY | POSITIVE SOLUTIONS

35J75 | 35B40 | 35R11 (primary) | LAPLACIAN | MATHEMATICS | LOCAL BEHAVIOR | BOUNDARY | POSITIVE SOLUTIONS

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2017, Volume 330, pp. 863 - 883

In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite...

Finite element method | Irregular domain | Riesz fractional derivative | Nonlinear source term | SPECTRAL METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DISCONTINUOUS GALERKIN METHODS | BOUNDED DOMAINS | DIFFERENCE APPROXIMATIONS | ADVECTION-DISPERSION EQUATIONS | PHYSICS, MATHEMATICAL | Methods | Algorithms | Yuan (China) | Analysis | Mathematics - Numerical Analysis

Finite element method | Irregular domain | Riesz fractional derivative | Nonlinear source term | SPECTRAL METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DISCONTINUOUS GALERKIN METHODS | BOUNDED DOMAINS | DIFFERENCE APPROXIMATIONS | ADVECTION-DISPERSION EQUATIONS | PHYSICS, MATHEMATICAL | Methods | Algorithms | Yuan (China) | Analysis | Mathematics - Numerical Analysis

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 04/2017, Volume 20, Issue 2, pp. 307 - 336

Since the 60s of last century Fractional Calculus exhibited a remarkable progress and presently it is recognized to be an important topic in the scientific...

01A61 | 01A60 | 60G22 | fractional calculus | development | Primary 26A33 | fractional order differential equations | fractional order mathematical models | 35R11 | 01A67 | Secondary 34A08 | applications | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Analysis | Calculus | Differentiation | Mathematical analysis | Fractional calculus

01A61 | 01A60 | 60G22 | fractional calculus | development | Primary 26A33 | fractional order differential equations | fractional order mathematical models | 35R11 | 01A67 | Secondary 34A08 | applications | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Analysis | Calculus | Differentiation | Mathematical analysis | Fractional calculus

Journal Article

7.
Full Text
Anti-symmetry of the second eigenfunction of the fractional Laplace operator in a 3-D ball

Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 2/2019, Volume 26, Issue 1, pp. 1 - 8

In this work we extend a recent result by Dyda et al. (J Lond Math Soc 95(2):500–518, 2017) to dimension 3.

Unit ball | Analysis | 35R11 | Mathematics | Fractional Laplacian | Anti-symmetry | Primary 35P15 | MATHEMATICS, APPLIED

Unit ball | Analysis | 35R11 | Mathematics | Fractional Laplacian | Anti-symmetry | Primary 35P15 | MATHEMATICS, APPLIED

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2016, Volume 19, Issue 5, pp. 1222 - 1249

Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than...

fractional-order derivative | image processing | fractional calculus | Primary 26A33 | 35R11 | 34K37 | Secondary 34A08 | Fractional-Order Derivative | Fractional calculus | MATHEMATICS, APPLIED | ENCRYPTION | RECOGNITION | MULTILEVEL ALGORITHM | MODEL | COUPLED NEURAL-NETWORK | MATHEMATICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | EDGE-DETECTION | FOURIER-TRANSFORM | DIFFUSION | DIFFERENTIATION | REGULARIZATION | Usage | Image processing | Mathematical analysis | Methods

fractional-order derivative | image processing | fractional calculus | Primary 26A33 | 35R11 | 34K37 | Secondary 34A08 | Fractional-Order Derivative | Fractional calculus | MATHEMATICS, APPLIED | ENCRYPTION | RECOGNITION | MULTILEVEL ALGORITHM | MODEL | COUPLED NEURAL-NETWORK | MATHEMATICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | EDGE-DETECTION | FOURIER-TRANSFORM | DIFFUSION | DIFFERENTIATION | REGULARIZATION | Usage | Image processing | Mathematical analysis | Methods

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 02/2019, Volume 22, Issue 1, pp. 128 - 138

Stable distributions are a class of distributions that have important uses in probability theory. They also have a applications in the theory of fractional...

stable distributions | Green’s function | 34K37 | fractional diffusions | Primary 35R11 | 60E07 | Secondary 34A08 | Thermodynamics | Probability theory

stable distributions | Green’s function | 34K37 | fractional diffusions | Primary 35R11 | 60E07 | Secondary 34A08 | Thermodynamics | Probability theory

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 03/2019, Volume 64, Issue 3, pp. 461 - 481

The aim of this paper is to study the existence solution for Schrödinger-Kirchhoff-type equations involving nonlocal p-fractional Laplacian where is a real...

35J60 | Primary: 35A15 | Mountain Pass Theorem | 35R11 | Integrodifferential operators | Schrödinger-Kirchhoff-type equation

35J60 | Primary: 35A15 | Mountain Pass Theorem | 35R11 | Integrodifferential operators | Schrödinger-Kirchhoff-type equation

Journal Article

Quaestiones Mathematicae, ISSN 1607-3606, 02/2020, Volume 43, Issue 2, pp. 185 - 192

This paper is devoted to the problem of existence of global solutions of the time-fractional Burgers equation. For certain initial-boundary problems for the...

blow-up of solution | 35R11 | fractional derivative | Primary 35K55 | non-existence of solution | Burgers equation

blow-up of solution | 35R11 | fractional derivative | Primary 35K55 | non-existence of solution | Burgers equation

Journal Article

Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 10/2018, Volume 25, Issue 5, pp. 1 - 43

In this paper we study the global (in time) existence of small data solutions to semi-linear fractional $$\sigma $$ σ -evolution equations with mass or power...

Secondary 35A01 | Global in time existence | Fractional equations | Analysis | sigma $$ σ -Evolution equations | Small data solutions | Mathematics | Primary 35R11

Secondary 35A01 | Global in time existence | Fractional equations | Analysis | sigma $$ σ -Evolution equations | Small data solutions | Mathematics | Primary 35R11

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 8/2016, Volume 55, Issue 4, pp. 1 - 25

We obtain nontrivial solutions to the Brezis–Nirenberg problem for the fractional p-Laplacian operator, extending some results in the literature for the...

Secondary 35A15 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35J92 | 35B33 | Mathematics | Primary 35R11 | EXISTENCE | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | R-N | INEQUALITIES | NONLINEARITY | POSITIVE SOLUTIONS | CRITICAL GROWTH | CRITICAL SOBOLEV EXPONENTS | ELLIPTIC-EQUATIONS

Secondary 35A15 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35J92 | 35B33 | Mathematics | Primary 35R11 | EXISTENCE | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | R-N | INEQUALITIES | NONLINEARITY | POSITIVE SOLUTIONS | CRITICAL GROWTH | CRITICAL SOBOLEV EXPONENTS | ELLIPTIC-EQUATIONS

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2019, Volume 22, Issue 5, pp. 1414 - 1436

In this paper we study the Dirichlet eigenvalue problem Here Ω is a bounded domain in ℝ , Δ is the standard local -Laplacian and Δ is a nonlocal -homogeneous...

Secondary 35J92 | fractional calculus | eigenvalues | 47G20 | Primary 35R11 | 35P30 | Laplacian | MATHEMATICS | MATHEMATICS, APPLIED | p-Laplacian | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIPLICITY | Eigenvalues | Dirichlet problem | Eigenvectors | Arrays | Eigen values

Secondary 35J92 | fractional calculus | eigenvalues | 47G20 | Primary 35R11 | 35P30 | Laplacian | MATHEMATICS | MATHEMATICS, APPLIED | p-Laplacian | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIPLICITY | Eigenvalues | Dirichlet problem | Eigenvectors | Arrays | Eigen values

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 04/2017, Volume 20, Issue 2, pp. 352 - 383

Most existing research on applying the finite element method to discretize space fractional operators is studied on regular domains using either uniform...

65M15 | finite element method | Primary 26A33 | Secondary 65M06 | two-dimensional time-space fractional wave equation | 35R11 | irregular domain | 65M12 | unstructured mesh | MATHEMATICS | SPECTRAL METHOD | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | APPROXIMATION | VOLUME | DIFFUSION | MODEL | Wave equation | Finite element method | Convex domains | Analysis | Brain | Operators | Numerical analysis | Weapons testing | Mathematical analysis | Stability analysis | Galerkin method | Finite element analysis | Nonlinear programming

65M15 | finite element method | Primary 26A33 | Secondary 65M06 | two-dimensional time-space fractional wave equation | 35R11 | irregular domain | 65M12 | unstructured mesh | MATHEMATICS | SPECTRAL METHOD | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | APPROXIMATION | VOLUME | DIFFUSION | MODEL | Wave equation | Finite element method | Convex domains | Analysis | Brain | Operators | Numerical analysis | Weapons testing | Mathematical analysis | Stability analysis | Galerkin method | Finite element analysis | Nonlinear programming

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 12/2011, Volume 71, Issue 4, pp. 583 - 600

We develop a kind of fractional calculus and theory of relaxation and diffusion equations associated with operators in the time variable, of the form...

complete Bernstein function | Primary 26A33 | Analysis | Secondary 60K05 | 35R11 | Differential-convolution operator | Stieltjes function | Mathematics | renewal process | relaxation equation | fundamental solution of the Cauchy problem | 34A08 | MATHEMATICS | ULTRASLOW DIFFUSION | DIFFERENTIAL-EQUATIONS | DISTRIBUTED-ORDER CALCULUS

complete Bernstein function | Primary 26A33 | Analysis | Secondary 60K05 | 35R11 | Differential-convolution operator | Stieltjes function | Mathematics | renewal process | relaxation equation | fundamental solution of the Cauchy problem | 34A08 | MATHEMATICS | ULTRASLOW DIFFUSION | DIFFERENTIAL-EQUATIONS | DISTRIBUTED-ORDER CALCULUS

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 02/2018, Volume 21, Issue 1, pp. 10 - 28

We obtain a generalized diffusion equation in modified or Riemann-Liouville form from continuous time random walk theory. The waiting time probability density...

33E12 | Mittag-Leffler functions | Primary 26A33 | 35R11 | continuous time random walk (CTRW) | anomalous diffusion | generalized diffusion equation | Secondary 34A08 | LANGEVIN EQUATION | MATHEMATICS, APPLIED | SERIES | DISPERSION | PRABHAKAR | MATHEMATICS | TRANSPORT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MODELS | Research | Heat equation | Random walks (Mathematics) | Mathematical research | Economic models | Mathematical analysis | Random walk | Random walk theory | Diffusion | Probability distribution functions | Probability density functions | Distribution functions

33E12 | Mittag-Leffler functions | Primary 26A33 | 35R11 | continuous time random walk (CTRW) | anomalous diffusion | generalized diffusion equation | Secondary 34A08 | LANGEVIN EQUATION | MATHEMATICS, APPLIED | SERIES | DISPERSION | PRABHAKAR | MATHEMATICS | TRANSPORT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MODELS | Research | Heat equation | Random walks (Mathematics) | Mathematical research | Economic models | Mathematical analysis | Random walk | Random walk theory | Diffusion | Probability distribution functions | Probability density functions | Distribution functions

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 04/2018, Volume 21, Issue 2, pp. 276 - 311

We discuss an initial-boundary value problem for a fractional diffusion equation with Caputo time-fractional derivative where the coefficients are dependent on...

weak solution | Primary 35R11 | initial-boundary value problem | regularity | fractional diffusion equation | Secondary 35K45, 26A33, 34A08 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SPACES | WEAK SOLUTIONS | Time dependence | Dirichlet problem | Boundary value problems

weak solution | Primary 35R11 | initial-boundary value problem | regularity | fractional diffusion equation | Secondary 35K45, 26A33, 34A08 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SPACES | WEAK SOLUTIONS | Time dependence | Dirichlet problem | Boundary value problems

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2018, Volume 21, Issue 5, pp. 1294 - 1312

In this paper, we prove that Caputo type linear fractional evolution equations do not have nonconstant periodic solutions. Then, we study asymptotically...

fractional evolution equations | 35R11 | Primary 34A08 | asymptotically periodic mild solutions | existence and uniqueness | Secondary 26A33 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Fixed points (mathematics) | Nonlinear programming | Asymptotic properties | Mathematical analysis | Linear evolution equations

fractional evolution equations | 35R11 | Primary 34A08 | asymptotically periodic mild solutions | existence and uniqueness | Secondary 26A33 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Fixed points (mathematics) | Nonlinear programming | Asymptotic properties | Mathematical analysis | Linear evolution equations

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 07/2016, Volume 139, pp. 211 - 217

In this paper, we show that soliton to the fractional Yamabe flow must have constant fractional order curvature.

Soliton | Fractional Yamabe problem fractional Yamabe flow | secondary 53A30 | MSC primary 35R11 | 53C44 | 53C21 | EXISTENCE | MATHEMATICS, APPLIED | PART I | Fractional Yamabe problem | CLASSIFICATION | SCALAR CURVATURE FLOW | LAPLACIAN | MATHEMATICS | fractional Yamabe flow | RICCI | CONVERGENCE | MANIFOLDS | Nonlinearity | Constants | Mathematical analysis | Curvature | Solitons

Soliton | Fractional Yamabe problem fractional Yamabe flow | secondary 53A30 | MSC primary 35R11 | 53C44 | 53C21 | EXISTENCE | MATHEMATICS, APPLIED | PART I | Fractional Yamabe problem | CLASSIFICATION | SCALAR CURVATURE FLOW | LAPLACIAN | MATHEMATICS | fractional Yamabe flow | RICCI | CONVERGENCE | MANIFOLDS | Nonlinearity | Constants | Mathematical analysis | Curvature | Solitons

Journal Article

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