We investigate the oscillatory chemical dynamics in a closed isothermal reaction system described by the reversible Lotka-Volterra model. This is a three-dimensional, dissipative, singular perturbation to the conservative Lotka-Volterra model, with the free energy serving as a global Lyapunov function. We will show that there is a natural distinction between oscillatory and non-oscillatory regi...

A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space L2(Ω)×C(0,T ),Ω = {(x,y) : √ x2+y2 ≤ a}, z = 0, and T <∞. The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class C([Ω]×[Ω]), while the kernel of Volterra integral term is a positive and continuous function that belongs to the class C[0,T ]. Also in...

and hosti 013.02.0 Abstract A numerical method based on an NM-set of general, hybrid of block-pulse function and Taylor series (HBT), is proposed to approximate the solution of nonlinear Volterra–Fredholm integral equations. The properties of HBT are first presented. Also, the operational matrix of integration together with Newton-Cotes nodes are utilized to reduce the computation of nonlinear ...

Abstract: This article focuses on obtaining analytical solutions for d-dimensional, parabolic Volterra integro-differential equations with different types of frictional memory kernel. Based on Laplace transform and Fourier transform theories, the properties of the Fox-H function and convolution theorem, analytical solutions for the equations in the infinite domain are derived under three fricti...

The unique solvability issues of the Cauchy problem with a fractional derivative is considered in case when coefficient at desired function continuous function. solution found an explicit form. uniqueness theorem proved. existence for to proved by reducing it Volterra equation second kind singularity kernel, and necessary sufficient conditions are obtained.

The paper studies the exact solution of two kinds generalized Fokker-Planck equations in which integral kernels are given either by distributed order function $k_{1}(t) = \int_{0}^{1} t^{-\mu}/\Gamma(1- \mu) d\mu$ or Prabhakar $k_{2}(\alpha, \gamma; \lambda; t) e^{-\gamma}_{\alpha, 1 - \mu}(\lambda; d\mu$, where is denoted as $e^{-\gamma}_{\alpha, t)$. Both these can be called fading memory fun...

The Laplace transform method is applied to study the semi-Hyers–Ulam–Rassias stability of a Volterra integro-differential equation second order. A general formulated first; then, some particular cases for function from kernel are considered.

We present a new temporal approximation scheme for the boundary integral formulation of time-dependent scattering problems which can be combined with either collocation or Galerkin approximation in space. It uses the backward-in-time framework introduced in [P. J. Davies and D. B. Duncan, Convolution Spline Approximations of Volterra Integral Equations, www.mathstat. strath.ac.uk/research/repor...

By using the theory of exponential dichotomy and Banach fixed point theorem, this paper is concerned with the problem of the existence and uniqueness of almost periodic solution in a harvesting Lotka-Volterra recurrent neural networks on time scales. To a certain extent, our work in this paper corrects the defect in [Y.G. Liu, B.B. Liu, S.H. Ling, The almost periodic solution of Lotka-Volterra ...