相关论文: Fractional reaction-diffusion equations

In this paper we consider space-time fractional telegraph equations, where the time derivatives are intended in the sense of Hilfer and Hadamard while the space fractional derivatives are meant in the sense of Riesz-Feller. We provide the…

Truncated Levy flights are stochastic processes which display a crossover from a heavy-tailed Levy behavior to a faster decaying probability distribution function (pdf). Putting less weight on long flights overcomes the divergence of the…

The fractional diffraction optics theory has been elaborated using the Green function technique. The optics-fractional equation describing the diffraction X-ray scattering by imperfect crystals has been derived as the fractional matrix…

In this paper, we extend the spectral method developed [Dechicha and Puel, 2023] to any dimension $d\geqslant 1$, in order to construct an eigen-solution for the Fokker-Planck operator with heavy tail equilibria, of the form…

We provide several regularity results for non-homogeneous drift-diffusion equations with applications to general dissipative SQG. Our results unify in a rather simple way several previously known results. We build the estimates on an…

We are interested in the time asymptotic location of the level sets of solutions to Fisher-KPP reaction-diffusion equations with fractional diffusion in periodic media. We show that the speed of propagation is exponential in time, with a…

In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized Fox--Wright function and the generalized M-series and…

In this paper, we propose the invariant subspace approach to find exact solutions of time-fractional partial differential equations (PDEs) with time delay. An algorithmic approach of finding invariant subspaces for the generalized…

Reaction-diffusion equations are one of the most common partial differential equations used to model physical phenomenon. They arise as the combination of two physical processes: a driving force $f(u)$ that depends on the state variable $u$…

Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by…

We consider bistable reaction-diffusion equations in funnel-shaped domains of R N made up of straight parts and conical parts with positive opening angles. We study the large time dynamics of entire solutions emanating from a planar front…

The fractional reaction diffusion equation u_t + Au = g(u) is discussed, where A is a fractional differential operator on the real line with order \alpha between 0 and 2, the C^1 function g vanishes at 0 and 1, and either g is non-negative…

We present a method for solving the reaction-diffusion equation with general potential in free space. It is based on the approximation of the Feynman-Kac formula by a sequence of convolutions on sequentially diminishing grids. For…

We consider similarity solutions of the generalized convection-diffusion-reaction equation with both space- and time-dependent convection, diffusion and reaction terms. By introducing the similarity variable, the reaction-diffusion equation…

Fractional (in time and in space) evolution equations defined on Dirichlet regular bounded open domains, driven by fractional integrated in time Gaussian spatiotemporal white noise, are considered here. Sufficient conditions for the…

Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. In some special cases…

In this paper, we investigate direct and inverse source problems for the diffusion equation with two-term generalized fractional derivative (Hilfer derivative) in a rectangular domain. Using spectral expansion method, we derive two-term…

This work investigates how we can extend the invariant subspace method to two-dimensional time-fractional non-linear PDEs. More precisely, the systematic study has been provided for constructing the various dimensions of the invariant…

The stochastic solution to diffusion equations with polynomial coefficients is called a Pearson diffusion. If the time derivative is replaced by a distributed fractional derivative, the stochastic solution is called a fractional Pearson…

Several classic problems for particles diffusing outside an arbitrary configuration of non-overlapping partially reactive spherical traps in three dimensions are revisited. For this purpose, we describe the generalized method of separation…