Fundamental Solutions to Time-Fractional Advection Diffusion Equation in a Case of Two Space Variables
Open Access
- 11 March 2014
- journal article
- research article
- Published by Hindawi Limited in Mathematical Problems in Engineering
- Vol. 2014, 1-7
- https://doi.org/10.1155/2014/705364
Abstract
The fundamental solutions to time-fractional advection diffusion equation in a plane and a half-plane are obtained using the Laplace integral transform with respect to timeand the Fourier transforms with respect to the space coordinatesand. The Cauchy, source, and Dirichlet problems are investigated. The solutions are expressed in terms of integrals of Bessel functions combined with Mittag-Leffler functions. Numerical results are illustrated graphically.
Keywords
This publication has 34 references indexed in Scilit:
- On Using Random Walks to Solve the Space-Fractional Advection-Dispersion EquationsJournal of Statistical Physics, 2006
- Finite difference approximations for fractional advection–dispersion flow equationsJournal of Computational and Applied Mathematics, 2004
- Numerical solution of the space fractional Fokker–Planck equationJournal of Computational and Applied Mathematics, 2003
- Fractional advection‐dispersion equation: A classical mass balance with convolution‐Fickian FluxWater Resources Research, 2000
- Lévy anomalous diffusion and fractional Fokker–Planck equationPhysica A: Statistical Mechanics and its Applications, 2000
- Anomalous diffusion and charge relaxation on comb model: exact solutionsPhysica A: Statistical Mechanics and its Applications, 2000
- Application of a fractional advection‐dispersion equationWater Resources Research, 2000
- The fractional‐order governing equation of Lévy MotionWater Resources Research, 2000
- Lévy flights in external force fields: Langevin and fractional Fokker-Planck equations and their solutionsPhysical Review E, 1999
- A fractional diffusion equation to describe Lévy flightsPhysics Letters A, 1998