The Wright functions as solutions of the time-fractional diffusion equation.
type: Item
instance of: scholarly article
title: The Wright functions as solutions of the time-fractional diffusion equation.
zbMATH Open document ID: 1053.35008
DOI: 10.1016/S0096-3003(02)00320-X
author: Gianni Pagnini
author: Francesco Mainardi
published in: Applied Mathematics and Computation
publication date: 2003-09-15T00:00:00Z
review text: The authors consider the Cauchy problem for the time-fractional diffusion equation obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order \(\beta\in (0,2)\). They use the Fourier-Laplace transforms to show that the fundamental solutions (Green functions) are higher transcendental functions of the Wright-type and can be interpreted as spatial probability density functions evolving in time with similarity properties. They also provide a general presentation of these functions in terms of Mellin-Barnes integrals useful for numerical computation.
reviewed by: Ismail Taqi Ali
Mathematics Subject Classification ID: 35A22
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 35S10
zbMATH DE Number: 1981433
zbMATH Keywords: Laplace transforms
zbMATH Keywords: Fourier transforms
zbMATH Keywords: Mellin-Barnes integrals
zbMATH Keywords: Mittag-Leffler functions
zbMATH Keywords: Wright functions
zbMATH Keywords: Fox \(H\)-functions
MaRDI profile type: Publication
cites work: Spectral analysis of fractional kinetic equations with random data.
cites work: Q5338397
cites work: Q5820721
cites work: Q4438490
cites work: Q4438451
cites work: Wright functions as scale-invariant solutions of the diffusion-wave equation
cites work: Fractional Calculus: Integral and Differential Equations of Fractional Order
cites work: Q4215107
cites work: Q4282622
cites work: The fundamental solutions for the fractional diffusion-wave equation
cites work: Fractional relaxation-oscillation and fractional diffusion-wave phenomena.
cites work: Fractals and fractional calculus in continuum mechanics
cites work: On Mittag-Leffler-type functions in fractional evolution processes
cites work: The fundamental solution of the space-time fractional diffusion equation
cites work: Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals.
cites work: Q3957222
cites work: Q4161583
cites work: The random walk's guide to anomalous diffusion: A fractional dynamics approach
cites work: Q4233638
cites work: Q3141895
cites work: Q4743083
cites work: Q3954626
full work available at URL: s0096-3003(02)00320-x
OpenAlex ID: W2043775240
description: scientific article; zbMATH DE number 1981433