In this paper, we study the existence and uniqueness of solutions for general fractional-time
parabolic equations of mixture type, and their probabilistic representations in terms of the …

This paper derives physically meaningful boundary conditions for fractional diffusion
equations, using a mass balance approach. Numerical solutions are presented, and …

We prove an optimal extension and trace theorem for Sobolev spaces of nonlocal operators.
The extension is given by a suitable Poisson integral and solves the corresponding nonlocal …

We investigate the first-passage dynamics of symmetric and asymmetric Lévy flights in semi-
infinite and bounded intervals. By solving the space-fractional diffusion equation, we …

In this paper, we deal with the inverse source problem of determining a source in a time-
fractional diffusion equation where data are given at a fixed time. This problem is ill-posed …

We develop a unified Petrov–Galerkin spectral method for a class of fractional partial
differential equations with two-sided derivatives and constant coefficients of the form D t 2 τ 0 …

We obtain L p estimates for fractional parabolic equations with space-time non-local
operators∂ t α uL u+ λ u= f in (0, T)× R d, where∂ t α u is the Caputo fractional derivative of …

Exponential relaxation to equilibrium is a typical property of physical systems, but
inhomogeneities are known to distort the exponential relaxation curve, leading to a wide …

We consider a class of a fractional-time stochastic equation defined on a bounded domain
and show that the presence of the time derivative induces a significant change in the …

We review recent advances in spectral and spectral element methods for a class of fractional
partial differential equations. We focus on linear advection–diffusion–reaction equations in …