The space-time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analysed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigate...

Abstract In this article we present a quantitative central limit theorem for the stochastic fractional heat equation driven by general Gaussian multiplicative noise, including cases of space–time white noise and white-colored with spatial covariance given Riesz kernel or bounded integrable function. We show that average over ball radius R converges, as tends to infinity, after suitable renormal...

The paper is concerned with the fractional extension of the Lauwerier formulation of the problem related to the temperature field description in a porous medium (sandstone) saturated with oil (strata). The boundary value problem for the fractional heat equation is solved by means of the Caputo differintegration operator D ∗ of order 0 < α ≤ 1 and the Laplace transform. The solution is obtained ...

Recently, Metzler et al. [Phys. Rev. Lett. 82, 3563 (1999)], introduced a fractional Fokker-Planck equation (FFPE) describing a subdiffusive behavior of a particle under the combined influence of external nonlinear force field, and a Boltzmann thermal heat bath. In this paper we present the solution of the FFPE in terms of an integral transformation. The transformation maps the solution of ordi...

Using multiple stochastic integrals and Malliavin calculus, we analyze the quadratic variations of a class of Gaussian processes that contains the linear stochastic heat equation on R driven by a non-white noise which is fractional Gaussian with respect to the time variable (Hurst parameter H) and has colored spatial covariance of α-Riesz-kernel type. The processes in this class are self-simila...

In this paper, a new fractional Riccati equation rational expansion method is proposed to establish new exact solutions for fractional differential equations. For illustrating the validity of this method, we apply it to the nonlinear fractional Sharma-TassoOlever (STO) equation, the nonlinear time fractional biological population model and the nonlinear fractional foam drainage equation. Compar...

the immiscible displacement of oil by water through a porous and permeable reservoir rock can be described by the use of a fractional flow curves (fw versus sw). water flooding project parameters can be obtained from the fractional flow curve. however, developing a representative fractional flow curve for a specific reservoir can be quite challenging when fluid and special core analysis data is...

The convergence of difference scheme for initial-boundary value problem the heat equation with concentrated capacity and time-dependent coefficient space derivatives, is considered. Fractional order rate estimate in a special discrete Sobolev norms, compatible smoothness solution, proved.