Error Bounds of a Finite Difference/Spectral Method for the Generalized Time Fractional Cable Equation

The new implicit finite difference method for the solution of time fractional advection-dispersion equation

In this paper, a numerical solution of time fractional advection-dispersion equations are presented.The new implicit nite dierence methods for solving these equations are studied. We examinepractical numerical methods to solve a class of initial-boundary value fractional partial dierentialequations with variable coecients on a nite domain. Stability, consistency, and (therefore) convergenceof t...

A New Implicit Finite Difference Method for Solving Time Fractional Diffusion Equation

In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...

Analytical Solution of Generalized Space-Time Fractional Cable Equation

In this paper, we consider generalized space-time fractional cable equation in presence of external source. By using the Fourier-Laplace transform we obtain the Green function in terms of infinite series in H-functions. The fractional moments of the fundamental solution are derived and their asymptotic behavior in the short and long time limit is analyzed. Some previously obtained results are c...

Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation

Implicit RBF Meshless Method for the Solution of Two-dimensional Variable Order Fractional Cable Equation

In the present work, the numerical solution of two-dimensional variable-order fractional cable (VOFC) equation using meshless collocation methods with thin plate spline radial basis functions is considered. In the proposed methods, we first use two schemes of order O(τ2) for the time derivatives and then meshless approach is applied to the space component. Numerical results obtained ...