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Unbounded solution space10/6/2023 To solve fractional advection–diffusion equation, Chen formulated a fully-discrete numerical method by using the classical finite difference method. introduced an approximation for the fractional advection–diffusion equation according to lattice Boltzmann method by Bhatnagar–Gross–Krook or multiple-relaxation time collision operators. ![]() Recently, researchers have used several numerical methods to solve approximate fractional advection–diffusion equation involving the Kansa method, the finite difference method, a moving least squares meshless, Laplace transform, Bernstein dual Petrov–Galerkin method, the finite volume method, and the local discontinuous Galerkin method. Ding and Jiang considered the fractional Laplacian operator for analytical solutions of multi-term time space fractional advection–diffusion equation with mixed boundary conditions on a finite domain in. The numerical method is presented by using a Lax–Wendroff-type time discretization procedure for solving the fractional advection–diffusion equation. Authors in developed an implicit meshless approach for numerical simulation of fractional advection–diffusion equation. provided the finite element method for the fractional advection–diffusion equation with non-homogeneous initial-boundary condition. ![]() Motivated by these significant applications, researchers have taken considerable efforts to solve advection–diffusion equation. ![]() Specifically, this type of partial differential equation is used to describe dispersion in two-dimensional tidal currents, transport of pollutants in the atmosphere, heat transfer in a draining film, dispersion in finite porous media, and water transfer in soils. Mathematical description of physical phenomena in which physical quantities are transferred inside a physical system due to diffusion and convection leads to the well-known advection–diffusion equation.
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