Subdiffusive fractional equations are not structurally stable with respect to spatial perturbations to the anomalous exponent (Phys. Rev. E 85, 031132 (2012)). The question arises of applicability of these fractional equations to model real world phenomena. To rectify this problem we propose the inclusion of the random death process into the random walk scheme from which we arrive at the modifi...

The model is a subdiffusion-type fractional degenerate parabolic equation. We consider two inverse source problems with power vertical diffusion coefficients, including the well-known Monin-Obukhov atmospheric model. Final-time over-determination condition posed. Solutions to both are expressed in series expansion. Numerical examples discussed.

We study the first passage time (FPT) problem in Levy type of anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation, we obtain an analytic expression for the FPT distribution which, in the large passage time limit, is characterized by a universal power law. Contrasting this power law with the asymptotic FPT distribution from another type of anomalous diffusion exe...

Exact expressions of velocity, temperature and mass concentration have been calculated for free convective flow of fractional MHD viscous fluid over an oscillating plate. Expressions of velocity have been obtained both for sine and cosine oscillations of plate. Corresponding fractional differential equations have been solved by using Laplace transform and inverse Laplace transform. The expressi...

We consider initial value/boundary value problems for fractional diffusion-wave equation: ∂ α t u(x, t) = Lu(x, t), where 0 < α ≤ 2, where L is a symmetric uniformly elliptic operator with t-independent smooth coefficients. First we establish the unique existence of ths weak solutions and the asymptotic behaviour as the time t goes to ∞ and the proofs are based on the eigenfunction expansions. ...

In this paper, we introduce the linear fractional self-attracting diffusion driven by a fractional Brownian motion with Hurst index 1/2 < H < 1, which is analogous to the linear self-attracting diffusion. For 1-dimensional process we study its convergence and the corresponding weighted local time. For 2-dimensional process, as a related problem, we show that the renormalized selfintersection lo...

We study a linear-quadratic optimal control problem involving a parabolic equation with fractional diffusion and Caputo fractional time derivative of orders s ∈ (0, 1) and γ ∈ (0, 1], respectively. The spatial fractional diffusion is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic operator. Thus, we consider an equivalent formulation with a quasi-stationary elliptic problem...

We study the regularity of a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. The precise model is ut = ∇·(u∇(−∆)−1/2u). For definiteness, the problem is posed in {x ∈ RN , t ∈ R} with nonnegative initial data u(x, 0) that are integrable and decay at infinity. Previous papers have established the existence of mass-preserving, nonnegative ...

In this paper, we obtain the regularized trace formulae for a diffusion operator, which includes conformable fractional derivatives of order ? (0 &lt; 1) instead ordinary in traditional operator by contour integration method. The results paper are great importance solving inverse problems and can be considered as partial generalizations.