The applied method of slowly varying amplitudes gives us the possibility to reduce the nonlinear vector integrodifferential wave equation of the electrical and magnetic vector fields to the amplitude vector nonlinear differential equations. Using this approximation, different orders of dispersion of the linear and nonlinear susceptibility can be estimated. Critical values of parameters to obser...

We consider a branching-selection system in R with N particles which give birth independently at rate 1 and where after each birth the leftmost particle is erased, keeping the number of particles constant. We show that, as N → ∞, the empirical measure process associated to the system converges in distribution to a deterministic measure-valued process whose densities solve a free boundary integr...

In this paper, we study a nonlinear time-fractional Volterra equation with nonsingular Mittag-Leffler kernel in Hilbert spaces. By applying the properties of functions and method eigenvalue expansion, give mild solution our problem. Our main tool here is using some Sobolev embeddings.