Related papers: G-fractional diffusion on bounded domains in $\mat…
In the recent literature, the g-subdiffusion equation involving Caputo fractional derivatives with respect to another function has been studied in relation to anomalous diffusions with a continuous transition between different subdiffusive…
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…
A version of fractional diffusion on bounded domains, subject to 'homogeneous Dirichlet boundary conditions' is derived from a kinetic transport model with homogeneous inflow boundary conditions. For nonconvex domains, the result differs…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
Many physical phenomena occur on domains that grow in time. When the timescales of the phenomena and domain growth are comparable, models must include the dynamics of the domain. A widespread intrinsically slow transport process is…
This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady…
We provide explicit classical solutions and stochastic analogues for distributed-order space-time fractional diffusion equations on bounded domains with zero exterior boundary conditions. We also show that our results still hold when the…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
A $g$--subdiffusion equation with fractional Caputo time derivative with respect to another function $g$ is used to describe a process of a continuous transition from subdiffusion with parameters $\alpha$ and $D_\alpha$ to subdiffusion with…
In this paper, after a brief review of the general theory concerning regularized derivatives and integrals of a function with respect to another function, we provide a peculiar fractional generalization of the $(1+1)$-dimensional Dodson's…
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…
Recently, in the paper: T. Koszto{\l}owicz and A. Dutkiewicz, Phys. Rev. E \textbf{104}, 014118 (2021) the $g$--subdiffusion equation with fractional Caputo time derivative with respect to another function $g$ has been considered. This…
In the present article, we study the diffusion equations with fractional time derivatives. The aim of this paper is to investigate the best possible regularity for the initial value/boundary value problems with non-homogeneous Dirichlet…
The partial differential equation of Gaussian diffusion is generalized by using the time-fractional derivative of distributed order between 0 and 1, in both the Riemann-Liouville (R-L) and the Caputo (C) sense. For a general distribution of…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are given as spatial-temporal homogeneous and isotropic random…
This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables, and…
In this paper, we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and an external force into account, which…
This is a review of statistical inference methodology for stochastic differential equations driven by fractional Brownian motion, otherwise called fractional diffusions. The first section reviews the theory needed to rigorously define them.…