Related papers: Explicit solutions to fractional diffusion equatio…
Stochastic space-time fractional diffusion equations often appear in the modeling of the heat propagation in non-homogeneous medium. In this paper, we firstly investigate the Mittag--Leffler Euler integrator of a class of stochastic…
Spherical Bessel functions appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different…
The fundamental solution of the fractional diffusion equation of distributed order in time (usually adopted for modelling sub-diffusion processes) is obtained based on its Mellin-Barnes integral representation. Such solution is proved to be…
This paper is devoted to the numerical analysis of a piecewise constant discontinuous Galerkin method for time fractional subdiffusion problems. The regularity of weak solution is firstly established by using variational approach and…
By using the Zubarev nonequilibrium statistical operator method, and the Liouville equation with fractional derivatives, a generalized diffusion equation with fractional derivatives is obtained within the Renyi statistics. Averaging in…
Fractional generalized Langevin equation with external force is used to model single-file diffusion. It is found that for external force that varies with power law the solution for such a fractional Langevin equation gives the correct short…
We present and analyze a space-time Petrov-Galerkin finite element method for a time-fractional diffusion equation involving a Riemann-Liouville fractional derivative of order $\alpha\in(0,1)$ in time and zero initial data. We derive a…
It is shown that the density of the ratio of two random variables with the same variance and joint Gaussian density satisfies a non stationary diffusion equation. Implications of this result for kernel density estimation of the condensed…
We present a unified integral framework based on the Fourier-Laplace transform evaluated along a vertical line in the complex plane. By identifying the moment-generating function (MGF) of a random variable with the weights of these…
Inverse initial and inverse source problems of a time-fractional differential equation with Bessel operator are considered. Results on existence and uniqueness of solutions to these problems are presented. The solution method is based on…
Despite its generality and powerful convergence properties, Milstein's method for functionals of spatially bounded stochastic differential equations is widely regarded as difficult to implement. This has likely prevented it from being…
Let $Y$ be a standard Gamma(k) distributed random variable, $k>0$, and let $X$ be an independent positive random variable. We prove that if $X$ has a hyperbolically monotone density of order $k$ ($HM_k$), then the distributions of $Y\cdot…
In this paper we investigate the variable coefficient two-sided fractional diffusion, advection, reaction equations on a bounded interval. It is known that the fractional diffusion operator may lose coercivity due to the variable…
A generalization of the Poisson distribution based on the generalized Mittag-Leffler function $E_{\alpha, \beta}(\lambda)$ is proposed and the raw moments are calculated algebraically in terms of Bell polynomials. It is demonstrated, that…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
In this paper we present solutions of evolution equations for inclusive distribution of gluons as produced by jet traversing quark-gluon plasma. We reformulate the original equations in such a form that the virtual and unresolved-real…
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…
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…
We explore the spectral properties of the time-dependent Maxwell's equations for a plane interface between a metamaterial represented by the Drude model and the vacuum, which fill respectively complementary half-spaces. We construct…
We consider an evolution equation whose time-diffusion is of fractional type and we provide decay estimates in time for the $L^s$-norm of the solutions in a bounded domain. The spatial operator that we take into account is very general and…