Heat kernel estimates for time fractional equations

DOI10.1515/forum-2017-0192zbMath1401.60088arXiv1708.05863OpenAlexW2963473848MaRDI QIDQ1791227

Jian Wang, Panki Kim, Takashi Kumagai, Zhen-Qing Chen

Publication date: 4 October 2018

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.05863

zbMATH Keywords

subordinatorDirichlet formheat kernel estimatesCaputo derivativetime fractional equation

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Stable stochastic processes (60G52) Local time and additive functionals (60J55) Transition functions, generators and resolvents (60J35)

Related Items

Fokker-Planck equation for Feynman-Kac transform of anomalous processes, TRANSITION DENSITIES OF SUBORDINATORS OF POSITIVE ORDER, Fractional equations via convergence of forms, Exact asymptotic formulas for the heat kernels of space and time-fractional equations, Critical parameters for reaction-diffusion equations involving space-time fractional derivatives, Heat kernel estimates for subordinate Markov processes and their applications, Estimates on the tail probabilities of subordinators and applications to general time fractional equations, Unified stochastic representation, well-posedness analysis, and regularity analysis for the equations modeling anomalous diffusions, Stochastic Maximum Principle for Subdiffusions and Its Applications, Asymptotics of fundamental solutions for time fractional equations with convolution kernels, Random time change and related evolution equations. Time asymptotic behavior, On a discrete scheme for time fractional fully nonlinear evolution equations, Stochastic representation of solution to nonlocal-in-time diffusion, Feynman--Kac Transform for Anomalous Processes, Time fractional Poisson equations: representations and estimates, On fractional heat equation, Fractional Cauchy problem on random snowflakes, Estimates of Dirichlet heat kernels for unimodal Lévy processes with low intensity of small jumps

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On two-dimensional random walk among heavy-tailed conductances
• Convergence to fractional kinetics for random walks associated with unbounded conductances
• Fractional kinetic equation for Hamiltonian chaos
• Random walks with infinite spatial and temporal moments
• Time fractional equations and probabilistic representation
• Lower tail probability estimates for subordinators and nondecreasing random walks
• Cauchy problem for fractional diffusion equations
• Asymptotic properties of some space-time fractional stochastic equations
• Heat kernel estimates for jump processes of mixed types on metric measure spaces
• The art of random walks.
• Stochastic model for ultraslow diffusion
• Green function estimates for subordinate Brownian motions: Stable and beyond
• Transition Density Estimates for Diffusion Processes on Post Critically Finite Self-Similar Fractals
• Limit theorems for continuous-time random walks with infinite mean waiting times
• Fractional kinetic equations: solutions and applications
• Heat kernel estimates for subordinate Brownian motions
• Stochastic models for fractional calculus
• Bernstein functions. Theory and applications