Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 11/2015, Volume 54, Issue 3, pp. 2785 - 2806

Journal Article

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

Advances in nonlinear analysis, ISSN 2191-950X, 2016, Volume 5, Issue 1, pp. 27 - 55

The purpose of this paper is mainly to investigate the existence of entire solutions of the stationary Kirchhoff type equations driven by the fractional

variational methods | 35A15 | 47G20 | 35J60 | Kirchhoff type equations | 35R11 | Fractional | multiple solutions | Laplacian | Fractional p-Laplacian | LAPLACIAN | MATHEMATICS | MATHEMATICS, APPLIED | SCHRODINGER-EQUATION | NONLINEARITIES | ELLIPTIC-EQUATIONS

variational methods | 35A15 | 47G20 | 35J60 | Kirchhoff type equations | 35R11 | Fractional | multiple solutions | Laplacian | Fractional p-Laplacian | LAPLACIAN | MATHEMATICS | MATHEMATICS, APPLIED | SCHRODINGER-EQUATION | NONLINEARITIES | ELLIPTIC-EQUATIONS

Journal Article

4.
Full Text
The first integral method for Wu–Zhang system with conformable time-fractional derivative

Calcolo, ISSN 1126-5434, 2015, Volume 53, Issue 3, pp. 475 - 485

In this paper, the first integral method is used to construct exact solutions of the time-fractional Wu–Zhang system. Fractional derivatives are described by...

Wu–Zhang system | Numerical Analysis | Conformable fractional derivative | First integral method | 35Qxx | 35R11 | Mathematics | Theory of Computation | MATHEMATICS | Wu-Zhang system | EQUATION | CALCULUS | Methods | Algebra | Derivatives | Partial differential equations | Mathematical analysis | Integrals | Exact solutions | Nonlinearity | Rings (mathematics)

Wu–Zhang system | Numerical Analysis | Conformable fractional derivative | First integral method | 35Qxx | 35R11 | Mathematics | Theory of Computation | MATHEMATICS | Wu-Zhang system | EQUATION | CALCULUS | Methods | Algebra | Derivatives | Partial differential equations | Mathematical analysis | Integrals | Exact solutions | Nonlinearity | Rings (mathematics)

Journal Article

Calculus of variations and partial differential equations, ISSN 1432-0835, 2013, Volume 49, Issue 1-2, pp. 795 - 826

We study the non-local eigenvalue problem $$\begin{aligned} 2\, \int \limits _{\mathbb{R }^n}\frac{|u(y)-u(x)|^{p-2}\bigl (u(y)-u(x)\bigr )}{|y-x|^{\alpha...

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | 35J60 | Analysis | Theoretical, Mathematical and Computational Physics | 35R11 | Mathematics | 35P30 | MATHEMATICS | EQUATIONS | MATHEMATICS, APPLIED | LAPLACE OPERATOR | 1ST EIGENVALUE | Calculus of variations

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | 35J60 | Analysis | Theoretical, Mathematical and Computational Physics | 35R11 | Mathematics | 35P30 | MATHEMATICS | EQUATIONS | MATHEMATICS, APPLIED | LAPLACE OPERATOR | 1ST EIGENVALUE | Calculus of variations

Journal Article

Mathematische Annalen, ISSN 0025-5831, 10/2019, Volume 375, Issue 1, pp. 687 - 736

We discuss fattening phenomenon for the evolution of sets according to their nonlocal curvature. More precisely, we consider a class of generalized curvatures...

35R11 | Mathematics, general | 35D40 | Mathematics | 53C44 | 58E12 | MATHEMATICS | EVOLUTION | MOTION | MEAN-CURVATURE | SETS

35R11 | Mathematics, general | 35D40 | Mathematics | 53C44 | 58E12 | MATHEMATICS | EVOLUTION | MOTION | MEAN-CURVATURE | SETS

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

Arabian Journal of Mathematics, ISSN 2193-5343, 9/2017, Volume 6, Issue 3, pp. 201 - 211

We study the nonexistence of nontrivial solutions for the nonlinear elliptic system $$\begin{aligned} \left\{ \begin{array}{lll} (-\Delta _x)^{\alpha...

35R11 | Mathematics, general | 35B53 | Mathematics | 35J70

35R11 | Mathematics, general | 35B53 | Mathematics | 35J70

Journal Article

Annali di matematica pura ed applicata, ISSN 1618-1891, 2017, Volume 196, Issue 6, pp. 2043 - 2062

By using the penalization method and the Ljusternik–Schnirelmann theory, we investigate the multiplicity of positive solutions of the following fractional...

Penalization method | 35A15 | 35J60 | Multiplicity of solutions | 35R11 | Mathematics, general | Mathematics | Nehari manifold | Supercritical problems | Fractional Laplacian | 45G05 | MATHEMATICS | MATHEMATICS, APPLIED | GROUND-STATES

Penalization method | 35A15 | 35J60 | Multiplicity of solutions | 35R11 | Mathematics, general | Mathematics | Nehari manifold | Supercritical problems | Fractional Laplacian | 45G05 | MATHEMATICS | MATHEMATICS, APPLIED | GROUND-STATES

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

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 8/2014, Volume 65, Issue 4, pp. 711 - 728

In this paper, we are concerned with nonlocal problem for fractional evolution equations with mixed monotone nonlocal term of the form...

34K30 | 35K90 | Nonlocal condition | Theoretical and Applied Mechanics | Monotone iterative method | Fractional evolution equation | Engineering | Mathematical Methods in Physics | Measure of noncompactness | Coupled lower and upper mild L -quasi-solutions | C 0 -semigroup | 35R11 | 47H07 | 47H08 | Mathematics Subject Classification : 34K30, 35K90, 35R11, 47H07, 47H08 | semigroup | Coupled lower and upper mild L-quasi-solutions | MATHEMATICS, APPLIED | C-0-semigroup | DIFFERENTIAL-EQUATIONS | CAUCHY-PROBLEM | INTEGRODIFFERENTIAL EQUATIONS | ITERATIVE TECHNIQUE | UNIQUENESS

34K30 | 35K90 | Nonlocal condition | Theoretical and Applied Mechanics | Monotone iterative method | Fractional evolution equation | Engineering | Mathematical Methods in Physics | Measure of noncompactness | Coupled lower and upper mild L -quasi-solutions | C 0 -semigroup | 35R11 | 47H07 | 47H08 | Mathematics Subject Classification : 34K30, 35K90, 35R11, 47H07, 47H08 | semigroup | Coupled lower and upper mild L-quasi-solutions | MATHEMATICS, APPLIED | C-0-semigroup | DIFFERENTIAL-EQUATIONS | CAUCHY-PROBLEM | INTEGRODIFFERENTIAL EQUATIONS | ITERATIVE TECHNIQUE | UNIQUENESS

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

Calculus of variations and partial differential equations, ISSN 1432-0835, 2010, Volume 42, Issue 1-2, pp. 21 - 41

We establish existence and non-existence results to the Brezis–Nirenberg type problem involving the square root of the Laplacian in a bounded domain with zero...

35J65 | Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | 35J60 | Theoretical, Mathematical and Computational Physics | Analysis | 35B99 | 35B33 | 35R11 | Mathematics | 58E30 | FRACTIONAL LAPLACIAN | OBSTACLE PROBLEM | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | POSITIVE SOLUTIONS | EQUATIONS | BOUNDARY | Boundary conditions | Dirichlet problem | Partial differential equations | Mathematical analysis | Calculus of variations | Roots

35J65 | Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | 35J60 | Theoretical, Mathematical and Computational Physics | Analysis | 35B99 | 35B33 | 35R11 | Mathematics | 58E30 | FRACTIONAL LAPLACIAN | OBSTACLE PROBLEM | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | POSITIVE SOLUTIONS | EQUATIONS | BOUNDARY | Boundary conditions | Dirichlet problem | Partial differential equations | Mathematical analysis | Calculus of variations | Roots

Journal Article

Advanced Nonlinear Studies, ISSN 1536-1365, 07/2017, Volume 17, Issue 3, pp. 429 - 456

This paper deals with the existence and the asymptotic behavior of nontrivial solutions for some classes of stationary Kirchhoff problems driven by a...

Stationary Kirchhoff-Dirichlet Problems | Nonlocal p-Laplacian Operators | Critical Nonlinearities | Variational Methods | Hardy Coefficients | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | BREZIS

Stationary Kirchhoff-Dirichlet Problems | Nonlocal p-Laplacian Operators | Critical Nonlinearities | Variational Methods | Hardy Coefficients | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | BREZIS

Journal Article

Manuscripta mathematica, ISSN 1432-1785, 2016, Volume 153, Issue 1-2, pp. 53 - 70

We consider here operators which are sum of (possibly) fractional derivatives, with (possibly different) order. The main constructive assumption is that the...

35R11 | 35R09 | 35B53 | MATHEMATICS | Mathematics - Analysis of PDEs

35R11 | 35R09 | 35B53 | MATHEMATICS | Mathematics - Analysis of PDEs

Journal Article

Mathematische Annalen, ISSN 0025-5831, 12/2016, Volume 366, Issue 3-4, pp. 941 - 979

Journal Article

International Journal of Nonlinear Sciences and Numerical Simulation, ISSN 1565-1339, 04/2018, Volume 19, Issue 2, pp. 215 - 222

In this paper, we deal with the existence of multiple nontrivial solutions for the following fractional -Laplacian Kirchhoff problems where parameter belongs...

45C05 | 58E05 | critical exponent | 35B33 | degenerate fractional Kirchhof-type problem | 35R11 | concentration–compactness principle

45C05 | 58E05 | critical exponent | 35B33 | degenerate fractional Kirchhof-type problem | 35R11 | concentration–compactness principle

Journal Article

Advances in Calculus of Variations, ISSN 1864-8258, 04/2016, Volume 9, Issue 2, pp. 101 - 125

We investigate a class of quasi-linear nonlocal problems, including as a particular case semi-linear problems involving the fractional Laplacian and arising in...

Morse theory | regularity of solutions | 35P15 | 35R11 | Fractional | existence and multiplicity of weak solutions | 35P30 | Laplacian problems | Fractional p-Laplacian problems | MATHEMATICS | MATHEMATICS, APPLIED | NONLINEAR EQUATIONS | REGULARITY | DIRICHLET PROBLEM | GUIDE | Game theory | Population biology | Phase transitions | Dynamic tests | Phase transformations | Dynamics | Mathematical analysis | Continuum mechanics | Topology | Calculus of variations

Morse theory | regularity of solutions | 35P15 | 35R11 | Fractional | existence and multiplicity of weak solutions | 35P30 | Laplacian problems | Fractional p-Laplacian problems | MATHEMATICS | MATHEMATICS, APPLIED | NONLINEAR EQUATIONS | REGULARITY | DIRICHLET PROBLEM | GUIDE | Game theory | Population biology | Phase transitions | Dynamic tests | Phase transformations | Dynamics | Mathematical analysis | Continuum mechanics | Topology | Calculus of variations

Journal Article

Quaestiones mathematicae, ISSN 1607-3606, 02/2020, pp. 1 - 18

Journal Article

Nonlinear Differential Equations and Applications, ISSN 1021-9722, 10/2015, Volume 22, Issue 3, pp. 477 - 497

Journal Article

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