Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

The probabilistic point of view on the generalized fractional PDES

Tools
- Tools
+ Tools

Kolokoltsov, V. N. (Vasiliĭ Nikitich) (2019) The probabilistic point of view on the generalized fractional PDES. Fractional Calculus and Applied Analysis, 22 (3). pp. 543-600. doi:10.1515/fca-2019-0033

[img]
Preview
PDF
WRAP-probabilistic-point-view-generalized-fractional-PDES-Kolokoltsov-2019.pdf - Accepted Version - Requires a PDF viewer.

Download (551Kb) | Preview
Official URL: https://doi.org/10.1515/fca-2019-0033

Request Changes to record.

Abstract

This paper aims at unifying and clarifying the recent advances in the analysis of the fractional and generalized fractional Partial Differential Equations of Caputo and Riemann-Liouville type arising essentially from the probabilistic point of view. This point of view leads to the path integral representation for the solutions of these equations, which is seen to be stable with respect to the initial data and key parameters and is directly amenable to numeric calculations (Monte-Carlo simulation). In many cases these solutions can be compactly presented via the wide class of operator-valued analytic functions of the Mittag-Leffler type, which are proved to be expressed as the Laplace transforms of the exit times of monotone Markov processes.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Fractional calculus, Differential equations, Differential equations, Partial
Journal or Publication Title: Fractional Calculus and Applied Analysis
Publisher: Bulgarian Academy of Sciences, Institute of Mathematics and Informatics
ISSN: 1311-0454
Official Date: 30 July 2019
Dates:
DateEvent
30 July 2019Published
29 May 2019Accepted
Volume: 22
Number: 3
Page Range: pp. 543-600
DOI: 10.1515/fca-2019-0033
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Copyright Holders: © 2019 Diogenes Co., Sofia
Related URLs:
  • Publisher

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics

twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us