In this paper, we establish some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two independent variables, and we present the applications to research the boundedness of solutions to retarded nonlinear Volterra-Fredholm type integral equations.

We obtain necessary conditions of optimality for impulsive Volterra integral equations with switching and impulsive controls, with variable impulse time-instants. The present work continues and complements our previous work on impulsive Volterra control with fixed impulse times.

The first passage time problem for Brownian motions hitting a barrier has been extensively studied in the literature. In particular, many incarnations of integral equations which link the density of the hitting time to the equation for the barrier itself have appeared. Most interestingly, Peskir (2002b) demonstrates that a master integral equation can be used to generate a countable number of n...

New results about the bound characteristics of both the generalized frequency response functions (GFRFs) and the output frequency response for the NARX (Nonlinear AutoRegressive model with eXogenous input) model are established. It is shown that the magnitudes of the GFRFs and the system output spectrum can all be bounded by a polynomial function of the magnitude bound of the first order GFRF, ...

We analyse the asymptotic behaviour of integro-differential equations modelling N populations in interaction, where interactions are modelled by non-local terms involving linear combinations of the total number of individuals in each population. These models have already been shown to be suitable for the modelling of drug resistance in cancer. They also generalise the usual Lotka-Volterra ordin...

In this paper, we first establish the existence of semi-traveling wave solutions to a diffusive generalized Holling-Tanner predator-prey model in which functional response may depend on both predator and prey populations. Then, by constructing Lyapunov function, apply obtained result show traveling models with various responses, including Lotka-Volterra type response, Holling ? Beddington-DeAng...

This paper is devoted to apply the Lie methods a class of reaction diffusion advection systems two interacting species u and v with arbitrary constitutive functions f g. The term appearing in equation for logistic function Lotka-Volterra type. Once obtained algebra any form g classification carried out. Interesting reduced are derived admitting wide classes exact solutions.

In this paper, a Jacobi-collocation spectral method is developed for Volterra integral equations of second kind with a weakly singular kernel. We use some function transformation and variable transformations to change the equation into a new Volterra integral equation defined on the standard interval [−1, 1], so that the solution of the new equation possesses better regularity and the Jacobi or...

We consider a bitrophic spatially distributed community consisting of prey and actively moving predators. The model is based on the assumption that the spatial and temporal variations of the predators' velocity are determined by the prey gradient. Locally, the populations follow the simple Lotka-Volterra interaction. We also assume predator reproduction and mortality to be negligible in compari...

In this paper, stochastic Volterra equations, particularly fractional, in Hilbert space are studied. Sufficient conditions for mild solutions to be strong solutions are provided. Several examples of Volterra equations having strong solutions are given, as well.