A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation

Abstract

Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the moving Kriging interpolation is developed for a two-dimensional time-fractional diffusion equation. The shape function and its derivatives are obtained by the moving Kriging interpolation technique. For possessing the Kronecker delta property, this technique is very efficient in imposing the essential boundary conditions. The governing time-fractional diffusion equations are transformed into a standard weak formulation by the Galerkin method. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard central difference method. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in detail.

Time fractional dual-phase-lag heat conduction equation

“…Jiang and Qi [28] derived a fractional thermal wave model of skin burns caused by spatial heating. The multi-term time-space fractional advection-diffusion equations on a finite domain were considered and the analytical solutions were derived by Jiang et al [29] The numerical methods of solving the diffusion equations have also been studied, such as the meshless method [30][31][32] and the numerical inverse Laplace transform method. [33] Some research on the fractional Cattaneo model and its applications can be found in Refs.…”

Exponential B-spline collocation method for numerical solution of the generalized regularized long wave equation

“…, B n+1 forms a basis for functions defined over the problem domain [a, b]. The exponential B-splines (4) and their first and second derivatives vanish outside the interval…”

Controllability of fractional-order Chua’s circuit

“…Recently, interest in fractional calculus has experienced rapid growth and we can find many papers about its theory and applications in mathematics, physics, mechanics, information engineering, electronic engineering, and control engineering. [10][11][12][13][14][15][16][17] As for the controllability of a fractional order dynamical system, there are some published papers. [18][19][20] However, we cannot find any contribution to the controllability of fractional order circuits, to our best knowledge, although it is also an important research field.…”