Related papers: Cauchy problem for general time fractional diffusi…
We study the existence of global weak solutions of a nonlinear transport-diffusion equation with a fractional derivative in the time variable and under some extra hypotheses, we also study some regularity properties for this type of…
We consider fractional diffusion equations and study the stability of the inverse problem of determining the time-dependent parameter in a source term or a coefficient of zero-th order term from observations of the solution at one point in…
An implicit finite difference method with non-uniform timesteps for solving the fractional diffusion equation in the Caputo form is proposed. The method allows one to build adaptive methods where the size of the timesteps is adjusted to the…
In this paper, we study both the direct and inverse random source problems associated with the multi-term time-fractional diffusion-wave equation driven by a fractional Brownian motion. Regarding the direct problem, the well-posedness is…
Based on the non-Markov diffusion equation taking into account the spatial fractality and modeling for the generalized coefficient of particle diffusion…
We consider a general form of reaction-dispersion equations with non-local dispersal and local reaction. Under some general conditions, we prove the non-existence of transition fronts, as well as some stretching properties at large time for…
The time-fractional diffusion equation is considered, where the time derivative is either of Caputo or Riemann-Liouville type. The solution of a general initial-boundary value problem with time-dependent boundary conditions over bounded and…
In this paper, we introduce and analyze a numerical scheme for solving the Cauchy-Dirichlet problem associated with fractional nonlinear diffusion equations. These equations generalize the porous medium equation and the fast diffusion…
We derive the explicit solution operator of an abstract Cauchy problem involving a time-variable coefficient and a fractional power of an almost sectorial operator. The time-variable coefficient is recovered by solving the inverse abstract…
We consider a class of porous medium type of equations with Caputo time derivative. The prototype problem reads as $\Dc u=-\A u^m$ and is posed on a bounded Euclidean domain $\Omega\subset\mathbb{R}^N$ with zero Dirichlet boundary…
The backward problem for subdiffusion equation with the fractional Riemann-Liouville time-derivative of order ? 2 (0; 1) and an arbitrary positive self-adjoint operator A is considered. This problem is ill-posed in the sense of Hadamard due…
The present paper deals with the numerical solution of time-fractional advection-diffusion equations involving the Caputo derivative with source term by means of an unconditionally stable implicit finite difference method on quasi-uniform…
Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order…
In this paper, we study the Cauchy problem of the fractional wave equation with time-dependent damping and the source nonlinearity $f(u)\approx |u|^p$: $$ \begin{cases} \partial_t^2u(t,x)+(-\Delta)^{\sigma/2} u(t,x)+b(t) \partial_t u(t,x)…
We derive a fundamental solution $\mathscr{E}$ to a space-fractional diffusion problem on the half-line. The equation involves the Caputo derivative. We establish properties of $\mathscr{E}$ as well as formulas for solutions to the…
We study a model that intermediates among the wave, heat, and transport equations. The approach considers the propagation of initial disturbances in a one-dimensional medium that can vibrate. The medium is nonlinear in such a form that…
We consider the initial/boundary value problem for the fractional diffusion and diffusion-wave equations involving a Caputo fractional derivative in time. We develop two "simple" fully discrete schemes based on the Galerkin finite element…
We study two new classes of inverse problems for a time-switched system in which a fractional wave equation (with Caputo derivative of order $\alpha \in (1,2)$) governs the dynamics on the interval $[0,a)$, and a fractional diffusion…
We study generalized diffusion-wave equation in which the second order time derivative is replaced by integro-differential operator. It yields time fractional and distributed order time fractional diffusion-wave equations as particular…
We present a general method of solving the Cauchy problem for multidimensional parabolic (diffusion type) equation with variable coefficients which depend on spatial variable but do not change over time. We assume the existence of the…