Sasaki–Ricci flow equation on five-dimensional Sasaki–Einstein space Yp,q

Five-Dimensional Space-Times

A brane in five - dimensional Minkowski space ∗

We discuss the propagation of gravity in five-dimensional Minkowski space in the presence of a four-dimensional brane. We show that there exists a solution to the wave equation that leads to a propagator exhibiting four-dimensional behavior at low energies (long distances) with five-dimensional effects showing up as corrections at high energies (short distances). We compare our results with pro...

Numerical Solution of Space-time Fractional two-dimensional Telegraph Equation by Shifted Legendre Operational Matrices

Fractional differential equations (FDEs) have attracted in the recent years a considerable interest due to their frequent appearance in various fields and their more accurate models of systems under consideration provided by fractional derivatives. For example, fractional derivatives have been used successfully to model frequency dependent damping behavior of many viscoelastic materials. They a...

An Implicit Difference-ADI Method for the Two-dimensional Space-time Fractional Diffusion Equation

Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...

Numerical Implementation of a Space-Transformation Approach for Solving the Three-Dimensional Flow Equation

This work is concerned with the numerical implementation of the space-transformation approach in porous media modeling. Space transformation is a mathematical approach that simplifies the study of multidimensional problems by reducing them to unidimensional ones. In particular, the implementation aspects considered in this work include (i) the development and testing of numerical space-transfor...