Related papers: Traveling Wave Solutions for Space-Time Fractional…
A large class of physically important nonlinear and nonhomogeneous evolution problems, characterized by advection-like and diffusion-like processes, can be usefully studied by a time-differential form of Kolmogorov's solution of the…
The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions…
We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional,…
The fractional diffusion-wave equation (FDWE) is a recent generalization of diffusion and wave equations via time and space fractional derivatives. The equation underlies Levy random walk and fractional Brownian motion and is foremost…
This paper is devoted to describing a linear diffusion problem involving fractional-in-time derivatives and self-adjoint integro-differential space operators posed in bounded domains. One main concern of our paper is to deal with singular…
In this paper, traveling wave solutions to the nonlinearly dispersive Schr\"odinger equation are given in the case of one-dimensional non-relativistic electron confined to a cylindrical quantum well. Investigations gave evidence to the…
Inspired by the works of \cite{baz2} and \cite{kian}, this study develops an abstract framework for analyzing differential equations with space-dependent fractional time derivatives and bounded operators. Within this framework, we establish…
We study the limits of the additive and derivative martingales of one-dimensional branching Brownian motion in a periodic environment. Then we prove the existence of pulsating travelling wave solutions of the corresponding F-KPP equation in…
We consider nonlinear nonlocal diffusive evolution equations, governed by fractional Laplace-type operators, fractional time derivative and involving porous medium type nonlinearities. Existence and uniqueness of weak solutions are…
Stability of the traveling wave solution to a general class of one-dimensional nonlocal evolution equations is studied in $L^2$-spaces, thereby providing an alternative approach to the usual spectral analysis with respect to the supremum…
The recently developed Wigner functional theory is used to formulate an evolution equation for arbitrary multi-photon states, propagating through a turbulent atmosphere under arbitrary conditions. The resulting evolution equation, which is…
We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…
In this article, we introduce a moving-frame approach to the geophysical equation of two-dimensional uniformly stratified rotational fluid in oceans and find a family of exact solutions containing ten arbitrary parameter functions.
Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These…
We study propagation of traveling waves in a blood filled elastic artery with an axially symmetric dilatation (an idealized aneurysm) in long-wave approximation.The processes in the injured artery are modelled by equations for the motion of…
Using the continuous limit approximation in the dynamical system we study a nonlinear partial differential equation which corresponds to the generalization of both the Fermi-Pasta-Ulam and the Frenkel-Kontorova models. This generalized…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish evolutions…
The evolution of the non-thermal emission emitted by pulsar wind nebulae is generally calculated using spatially-independent particle transport models. Although useful, these models implicitly assume that the source of non-thermal particles…