Heat kernel of fractional Laplacian in cones

Krzysztof Bogdan; Tomasz Grzywny

Displaying similar documents to “Heat kernel of fractional Laplacian in cones”

Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition

Yuriy Povstenko (2014)

Open Mathematics

Similarity:

The central symmetric time-fractional heat conduction equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the boundary, and the physical condition with the prescribed linear combination of values of temperature and values of the heat flux at the boundary, which is a consequence of Newton’s law...

Pseudo-processes governed by higher-order fractional differential equations.

Beghin, Luisa (2008)

Electronic Journal of Probability [electronic only]

Similarity:

Reachability of cone fractional continuous-time linear systems

Tadeusz Kaczorek (2009)

International Journal of Applied Mathematics and Computer Science

Similarity:

A new class of cone fractional continuous-time linear systems is introduced. Necessary and sufficient conditions for a fractional linear system to be a cone fractional one are established. Sufficient conditions for the reachability of cone fractional systems are given. The discussion is illustrated with an example of linear cone fractional systems.

Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations

Hahn, Marjorie, Umarov, Sabir (2011)

Fractional Calculus and Applied Analysis

Similarity:

MSC 2010: 26A33, 35R11, 35R60, 35Q84, 60H10 Dedicated to 80-th anniversary of Professor Rudolf Gorenflo There is a well-known relationship between the Itô stochastic differential equations (SDEs) and the associated partial differential equations called Fokker-Planck equations, also called Kolmogorov equations. The Brownian motion plays the role of the basic driving process for SDEs. This paper provides fractional generalizations of the triple relationship between the driving...

On the Lauwerier formulation of the temperature field problem in oil strata.

Boyadjiev, Lyubomir, Kamenov, Ognian, Kalla, Shyam (2005)

International Journal of Mathematics and Mathematical Sciences

Similarity:

Heat kernel estimates for critical fractional diffusion operators

Longjie Xie, Xicheng Zhang (2014)

Studia Mathematica

Similarity:

We construct the heat kernel of the 1/2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.

Fractional flux and non-normal diffusion.

Abdennadher, Ali, Neel, Marie-Christine (2007)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Similarity:

Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems

Tadeusz Kaczorek (2013)

International Journal of Applied Mathematics and Computer Science

Similarity:

Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.

Heat Kernel : rencontre entre physiciens et mathématiciens

G. A. Vilkovisky (1992)

Recherche Coopérative sur Programme n°25

Similarity:

On one class of operators associated with differential equations of fractional order.

Aleroev, T.S. (2005)

Sibirskij Matematicheskij Zhurnal

Similarity:

Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian

Krzysztof Bogdan, Paweł Sztonyk (2007)

Studia Mathematica

Similarity:

We characterize those homogeneous translation invariant symmetric non-local operators with positive maximum principle whose harmonic functions satisfy Harnack's inequality. We also estimate the corresponding semigroup and the potential kernel.

Exact solution of impulse response to a class of fractional oscillators and its stability.

Li, Ming, Lim, S.C., Chen, Shengyong (2011)

Mathematical Problems in Engineering

Similarity:

Nonlinear Time-Fractional Differential Equations in Combustion Science

Pagnini, Gianni (2011)

Fractional Calculus and Applied Analysis

Similarity:

MSC 2010: 34A08 (main), 34G20, 80A25 The application of Fractional Calculus in combustion science to model the evolution in time of the radius of an isolated premixed flame ball is highlighted. Literature equations for premixed flame ball radius are rederived by a new method that strongly simplifies previous ones. These equations are nonlinear time-fractional differential equations of order 1/2 with a Gaussian underlying diffusion process. Extending the analysis to self-similar...

Stability analysis of fractional differential systems with order lying in $(1, 2)$ .

Zhang, Fengrong, Li, Changpin (2011)

Advances in Difference Equations [electronic only]

Similarity:

Positive stable realizations of fractional continuous-time linear systems

Tadeusz Kaczorek (2011)

International Journal of Applied Mathematics and Computer Science

Similarity:

Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.