A finite element method for time fractional partial differential equations

Fractional differential equations, particularly fractional partial differential equations (FPDEs) have many applications in areas such as diffusion processes, electromagnetics, electrochemistry, material science and turbulent flow. There are lots of work for the existence and uniqueness of the solutions for fractional partial differential equations. In recent years, people start to consider the numerical methods for solving fractional partial differential equation. The numerical methods include finite difference method, finite element method and the spectral method. In this dissertation, we mainly consider the finite element method, for the time fractional partial differential equation. We consider both time discretization and space discretization. We obtain the optimal error estimates both in time and space. The numerical examples demonstrate that the numerical results are consistent with the theoretical results

A Fractional Lie Group Method For Anomalous Diffusion Equations

Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method. A space-time fractional diffusion equation is used as an example to illustrate the effectiveness of the Lie group method.Comment: 5 pages,in pres

Fractional Variational Iteration Method for Fractional Nonlinear Differential Equations

Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to overcome such shortcomings, a fractional variational iteration method is proposed. The Lagrange multipliers can be identified explicitly based on fractional variational theory.Comment: 12 pages, 1 figure

Existence and uniqueness of a positive solution to generalized nonlocal thermistor problems with fractional-order derivatives

In this work we study a generalized nonlocal thermistor problem with fractional-order Riemann-Liouville derivative. Making use of fixed-point theory, we obtain existence and uniqueness of a positive solution.Comment: Submitted 17-Jul-2011; revised 09-Oct-2011; accepted 21-Oct-2011; for publication in the journal 'Differential Equations & Applications' (http://dea.ele-math.com