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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
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
Journal Article
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 08/2016, Volume 19, Issue 4, pp. 806 - 831
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
Journal Article
by Yang, Z and Yuan, Z and Nie, Y and Wang, J and Zhu, X and Liu, F
Journal of Computational Physics, ISSN 0021-9991, 02/2017, Volume 330, pp. 863 - 883
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
Journal Article
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
Journal Article
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2016, Volume 19, Issue 5, pp. 1222 - 1249
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
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
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
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
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 8/2016, Volume 55, Issue 4, pp. 1 - 25
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
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
Journal Article
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
Journal Article
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2018, Volume 21, Issue 5, pp. 1294 - 1312
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 07/2016, Volume 139, pp. 211 - 217
Journal Article
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