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 fractional diffusion equation is derived from the master equation of continuous time random walks (CTRWs) via a straightforward application of the GnedenkoKolmogorov limit theorem. The Cauchy problem for the fractional diffusion equation is solved in various important and general cases. The meaning of the proper diffusion limit for CTRWs is discussed.

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations with the averaging with respect to fast variable is used. The main assumption is that the correlator of probability densities of particles to make a step has a power-law dependence. As a result,...

In this paper, we introduce a new approach to solving fractional initial and boundary value problems involving heat equation, wave telegraph equation by modifying the double Sumudu transform of type. We discuss modified conformable together with conditions for its existence. addition, prove some more properties fractional-type transform, including convolution other properties, which are well kn...

Abstract. In this paper we study the controllability of an Euler Implicit time discrete heat equation in a bounded domain with a local internal controller. We prove that, based on Lebeau-Robbiano’s time iteration method, the projection in appropriate filtered space is null controllable with uniformly bounded control. In this way, the well-known null-controllability property of the heat equation...

In this article, we establish a probabilistic representation for the second-order moment of the solution of stochastic heat equation in [0,1]×R , with multiplicative noise, which is fractional in time and colored in space. This representation is similar to the one given in [8] in the case of an s.p.d.e. driven by a Gaussian noise, which is white in time. Unlike the formula of [8], which is base...

In this paper an inverse problem for the space fractional heat conduction equation is investigated. Firstly, we describe the approximate solution of the direct problem. Secondly, for the inverse problem part, we define the functional illustrating the error of approximate solution. To recover the thermal conductivity coefficient we need to minimize this functional. In order to minimize this func...