Work

Explicit solutions of some fractional partial differential equations via stable subordinators

Year: 2006

Type: article

Abstract: The aim of this work is to represent the solutions of one‐dimensional fractional partial differential equations (FPDEs) of order ( α ∈ ℝ + \ ℕ ) in both quasi‐probabilistic and probabilistic ways. The canonical processes used are generalizations of stable Lévy processes. The fundamental solutions of the fractional equations are given as functionals of stable subordinators. The functions used generalize the functions given by the Airy integral of Sirovich (1971). As a consequence of this representation, an explicit form is given to the density of the 3/2‐stable law and to the density of escaping island vicinity in vortex medium. Other connected FPDEs are also considered.

Source: International Journal of Stochastic Analysis

DOI: 10.1155/jamsa/2006/93502

Author: Latifa Debbi

Institutions: Institut Élie Cartan de Lorraine, University Ferhat Abbas of Setif, University Mohamed Boudiaf of M'sila, Université Henri Poincaré

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W2030453393

FWCI: 0.226

Cites: 28

Cited by: 17

Related to: 10