The fractional Fokker-Planck equation is often used to characterize anomalous diffusion. In this paper, a fully discrete approximation for the nonlinear spatial fractional Fokker-Planck equation is given, where the discontinuous Galerkin finite element approach is utilized in time domain and the Galerkin finite element approach is utilized in spatial domain. The priori error estimate is derived...

In this paper, two finite difference/element approaches for the time-fractional subdiffusion equation with Dirichlet boundary conditions are developed, in which the time direction is approximated by the fractional linear multistep method and the space direction is approximated by the finite element method. The two methods are unconditionally stable and convergent of order O(τq + hr+1) in the L2...

Numerical computations of frequency domain field problems or elliptical partial differential equations may be based on differential equations or integral equations. The new concept of field computation presented in this paper is based on the postulate of the existence of linear equations of the discretized nodal values of the fields, different from the conventional equations, but leading to the...

A finite difference scheme is produced when the partial derivatives in the partial differential equation(s) governing a physical phenomenon are replaced by a finite difference approximation. The result is a single algebraic equation or a system of algebraic equations which, when solved, provide an approximation to the solution of the original partial differential equation at selected points of ...

In this paper, a numerical efficient method is proposed for the solution of time fractional mobile/immobile equation. The fractional derivative of equation is described in the Caputo sense. The proposed method is based on a finite difference scheme in time and Legendre spectral method in space. In this approach the time fractional derivative of mentioned equation is approximated by a scheme of ord...

and Applied Analysis 3 Baeumer et al. 8, 13 have proved existence and uniqueness of a strong solution for 1.2 using the semigroup theory when f x, t, u is globally Lipschitz continuous. Furthermore, when f x, t, u is locally Lipschitz continuous, existence of a unique strong solution has also been shown by introducing the cut-off function. Finite difference methods have been studied in 14–16 fo...

In this article we have applied a numerical finite difference method to solve the Black-Scholes European and American option pricing both presented by fractional differential equations in time and asset.

In this paper, we investigate the existence of solution for a k-dimensional system of three points nabla fractional finite difference equations. Also, we present an example to illustrate our result.