相关论文: Comparison principles for the time-fractional diff…

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…

We consider the initial boundary value problem for the Einstein vacuum equations in the maximal gauge, or more generally, in a gauge where the mean curvature of a timelike foliation is fixed near the boundary. We prove the existence of…

The problem of blow up of solutions to the initial boundary value problem for non-autonomous semilinear wave equation with damping and accelerating terms under the Robin boundary condition is studied. Sufficient conditions of blow up in a…

In this work, we consider a number of boundary-value problems for time-fractional heat equation with the recently introduced Caputo-Fabrizio derivative. Using the method of separation of variables, we prove a unique solvability of the…

We prove existence of solutions for a nonlinear fractional oscillator equation with both left Riemann-Liouville and right Caputo fractional derivatives subject to natural boundary conditions. The proof is based on a transformation of the…

We present a general framework for the rigorous numerical analysis of time-fractional nonlinear parabolic partial differential equations, with a fractional derivative of order $\alpha\in(0,1)$ in time. The framework relies on three…

We aim to prove a unique solvability of an initial-boundary value problem (IBVP) for a time-fractional wave equation in a rectangular domain. We exploit the spectral expansion method as the main tool and used the solution to Cauchy problems…

Reaction-Diffusion systems arise in diverse areas of science and engineering. Due to the peculiar characteristics of such equations, analytic solutions are usually not available and numerical methods are the main tools for approximating the…

This paper focuses on a drift-diffusion system subjected to boundedly non dissipative Robin boundary conditions. A general existence result with large initial conditions is established by using suitable L1, L2 and trace estimates. Finally,…

A fast two-level linearized scheme with unequal time-steps is constructed and analyzed for an initial-boundary-value problem of semilinear subdiffusion equations. The two-level fast L1 formula of the Caputo derivative is derived based on…

This article aims to investigate the semi-classical analog of the general Caputo-type diffusion equation with time-dependent diffusion coefficient associated with the discrete Schr\"{o}dinger operator,…

We investigate quantitative properties of nonnegative solutions $u(t,x)\ge 0$ to the nonlinear fractional diffusion equation, $\partial_t u + \mathcal{L}F(u)=0$ posed in a bounded domain, $x\in\Omega\subset \mathbb{R}^N$, with appropriate…

A generalized Neumann solution for the two-phase fractional Lam\'e--Clapeyron--Stefan problem for a semi--infinite material with constant initial temperature and a particular heat flux condition at the fixed face is obtained, when a…

This paper deals with numerical solutions to a partial differential equation of fractional order. Generally this type of equation describes a transition from anomalous diffusion to transport processes. From a phenomenological point of view,…

For $\nu,\nu_i,\mu_j\in(0,1)$, we analyze the semilinear integro-differential equation on the one-dimensional domain $\Omega=(a,b)$ in the unknown $u=u(x,t)$ \[…

This paper is devoted to an in deep investigation of the first fundamental solution to the linear multi-dimensional space-time-fractional diffusion-wave equation. This equation is obtained from the diffusion equation by replacing the first…

In practice many problems related to space/time fractional equations depend on fractional parameters. But these fractional parameters are not known a priori in modelling problems. Hence continuity of the solutions with respect to these…

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…

Time-fractional semilinear and quasilinear parabolic equations with a Caputo time derivative of order $\alpha\in(0,1)$ are considered, solutions of which exhibit a singular behaviour at an initial time of type $t^\sigma$ for any fixed…

Initial-boundary value problems for second order fully nonlinear PDEs with Caputo time fractional derivatives of order less than one are considered in the framework of viscosity solution theory. Associated boundary conditions are Dirichlet…