Abdul Khaliq Dept. of Mathematical & Computational Sciences MTSUUSA In this talk we consider distributed order time space anomalous diffusion with nonhomogenous boundary conditions. Time fractional derivative is defined in Caputo sense and Matrix Transfer Technique (MTT) is utilized for fractional spatial discretization. Midpoint quadrature rule is applied to approximate the spatial integral term. Numerical experiments are presented by employing a recently developed splitstep method for space fractional reaction diffusion equations. Computational complexity and efficiency of the method is discussed as well as reliability and stability. 
Ali Dogru Saudi Aramco Fellow Saudi Arabia Gigantic reservoirs contribute significantly to meet the world energy demand. The PDEs are discretized both space and time resulting in discrete nonlinear equations which are solved by iterative methods. Because of the large size of the reservoirs, the number of computational elements are generally in the order of millions to billions or more. Solving such systems requires specific numerical methods and evolving computer hardware technology utilizing hundreds of thousands of CPUs and GPUS. 
Hongwei Liu EXPEC ARC, GPT Saudi ARAMCOKSA Physical experiments show wave amplitudes attenuation linearly increase with respect to frequencies for certain materials, including many types of rocks studied in geophysics. However, a long standing problem is there is no time domain wave equation to precisely describe this type of attenuation, despite many approximations having been proposed. We present a simple time domain wave equation to precisely simulate such linear attenuation (i.e., both dissipations and dispersions). The key idea is to represent the wavefield (the function to be solved) by complex value functions, rather than by real value functions which all previous time domain wave equations have employed For verification, we have compared CWE numerical solutions with analytical solutions for acoustic waves in constant velocity media, and obtained nearly perfect matching between these two solutions. 
Huangxin Chen The School of Mathematical Sciences Xiamen UniversityChina In this talk, we will present mixed finite element methods for spacefractional partial differential equations for flow and transport in fractured porous media. For the flow in fractured porous media, a spacefractional Darcy’s law will be introduced and it motivate us to use mixed finite element method for the flow by coupling the fractional Darcy’s law and mass conservation law. The massconservative property of the numerical scheme is naturally obtained which is important for the simulation of transport in fractured porous media. Then an upwind mixed finite element method will be introduced to simulate the transport with a fractional diffusion in fractured porous media. Performance of our schemes including numerical stability and solution accuracy will also be discussed. 
SHUYU SUN Earth Sciences & Engineering KAUSTKSA
In this talk we will introduce a kind
of spacefractional partial differential equations to model and
simulate the flow and transport in fractured porous media.
Firstly, we will introduce a spacefractional Darcy’s law for
the flow in fractured porous media, which is coupled with the
mass conservation law to model the porous media flow. The
new fractional partial differential equations for flow (and
transport) in fractured porous media is more physical than
that in literature; in particular, our formulation satisfies the
principle of Galilean invariance. We will also compare our new
model with the discrete fracture model and with the dual
porosity dual permeability model for flow (and transport) in
fractured porous media. 
Vu Kim Tuan Dept.of Mathematics University of West GeorgiaUSA In this talk we consider a fractional diffusion process on a finite length rod modeled by
We are concerned with the recovery of the diffusion
coefficient
from
the measurement of the flux at one end of the rod only. This
problem is close in spirit with the boundary control, where
is
a given input on the boundary and we can observe its
response. However the boundary control method is usually
applied to wave equations because of their finite wave speed
propagation. We prove that we can uniquely recover
from
a single boundary measurement and provide a constructive
procedure for its recovery. The algorithm is based on the
well known GelfandLevitanGasymov inverse spectral theory
of SturmLiouville operators and the Laplace transform
method. More precisely, we have.

YangQuan Chen MESA Lab of University of CaliforniaUSA 