Censored stable subordinators and fractional derivatives

DOI10.1515/fca-2021-0045zbMath1498.26009arXiv1906.07296OpenAlexW3095859285MaRDI QIDQ2236847

Zirui Xu, Qiang Du, Lorenzo Toniazzi

Publication date: 26 October 2021

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.07296

zbMATH Keywords

Mittag-Leffler functionfractional initial value problemfractional relaxation equationcensored stable subordinator

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Anomalous diffusion models (subdiffusion, superdiffusion, continuous-time random walks, etc.) (60K50)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Which functions are fractionally differentiable?
• Space-time fractional diffusion on bounded domains
• Fractional models of anomalous relaxation based on the Kilbas and Saigo function
• Ten equivalent definitions of the fractional Laplace operator
• Analysis of a nonlocal-in-time parabolic equation
• Convergence to fractional kinetics for random walks associated with unbounded conductances
• Predicting the ultimate supremum of a stable Lévy process with no negative jumps
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Fractals and fractional calculus in continuum mechanics
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Censored stable processes
• Generalised fractional evolution equations of Caputo type
• A fractional kinetic process describing the intermediate time behaviour of cellular flows
• Limit theorems for coupled continuous time random walks.
• Infinite divisibility of random variables and their integer parts
• Stochastic representation of solution to nonlocal-in-time diffusion
• What is the fractional Laplacian? A comparative review with new results
• The probabilistic point of view on the generalized fractional partial differential equations
• A smooth solution of a singular fractional differential equation
• Introduction to fractional and pseudo-differential equations with singular symbols
• Fractional-order operators: boundary problems, heat equations
• Hitting distributions of \(\alpha\)-stable processes via path censoring and self-similarity
• Introductory lectures on fluctuations of Lévy processes with applications.
• Lévy matters III. Lévy-type processes: construction, approximation and sample path properties
• Comparing Fréchet and positive stable laws
• A strong and weak approximation scheme for stochastic differential equations driven by a time-changed Brownian motion
• On the probabilistic approach to the solution of generalized fractional differential equations of Caputo and Riemann-Liouville type
• Nonlocal Modeling, Analysis, and Computation
• Limit theorems for continuous-time random walks with infinite mean waiting times
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• From Brownian Motion to Schrödinger’s Equation
• Mittag-Leffler Functions, Related Topics and Applications
• Clustered continuous-time random walks: diffusion and relaxation consequences
• Fundamental equations of branching Markov processes
• A construction of markov processes by piecing out
• Limit theorems for occupation times of Markov processes
• Bernstein functions. Theory and applications
• Stochastic models for fractional calculus

This page was built for publication: Censored stable subordinators and fractional derivatives