in this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. we utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. by using bernstein polynomial basis, the problem is transformed in...

Numerical method for Cahn-Hilliard equation has been well-studied, but few can be generalized to fractional Cahn-Hilliard equation. In this project to modified the numerical method proposed by Brian Wetton et al in the paper High accuracy solutions to energy gradient flows from material science models[1]. The method they described in the paper is a pseudo-spectral method suitable for considerin...

in this paper, we introduce a family of fractional-order chebyshev functions based on the classical chebyshev polynomials. we calculate and derive the operational matrix of derivative of fractional order $gamma$ in the caputo sense using the fractional-order chebyshev functions. this matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

the performance of water flooding can be investigated by using either detail numerical modeling or simulation, or simply through the analytical buckley-leverett (bl) model. the buckley-leverett analytical technique can be applied to one-dimensional homogeneous systems. in this paper, the impact of heterogeneity on water flooding performance and fractional flow curve is investigated. first, a ba...

The rst part of this thesis concerns the formulation of numerical methods that are local in time for the solution of equations with memory. The main idea is that the solution will be updated in the Fourier domain in order to avoid evaluating time convolution integrals that have memory. This work was made possible by the development of a good quadrature[31] of the Fourier integral where a small ...

The rst part of this thesis concerns the formulation of numerical methods that are local in time for the solution of equations with memory. The main idea is that the solution will be updated in the Fourier domain in order to avoid evaluating time convolution integrals that have memory. This work was made possible by the development of a good quadrature[31] of the Fourier integral where a small ...

In this article, we present an efficient local meshless method for the numerical treatment of 3-D convection-diffusion PDE. The demand techniques increment because its nature and simplicity usage in higher dimensions. This technique approximates solution on set uniform scattered nodes. space derivatives models are discretized by proposed procedure though time fractional part is Liouville-Caputo...

This paper is devoted to the analysis of the problem of controllability of fractional (in time) Ordinary and Partial Differential Equations (ODE/PDE). The fractional time derivative introduces some memory effects on the system that need to be taken into account when defining the notion of control. In fact, in contrast with the classical ODE and PDE control theory, when driving these systems to ...