In this note, we obtain a new multiplicative perturbation theorem for local Cregularized cosine function with a nondensely defined generator A. An application to an integrodifferential equation is given.

We prove the unique solvability of boundary-value problem for a loaded third-order integrodifferential equation with parabolic-hyperbolic operator. By method integral equations, we existence and uniqueness solutions problems.

Bumble bees may possess a scalar character called dominance, which changes according to certain rules as a result of encounters between pairs of organisms. An equation for the distribution of dominance in a population is derived based on a set of plausible axioms. The resulting Boltzmann-like integrodifferential equation is analyzed, analytically and/or numerically, for certain important specia...

In this paper, we propose the Chebyshev wavelet approximation for the numerical solution of a class of integrodifferential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields. We show that the Chebyshev approximation transform an integral equation to an explicit system of linear algebraic equations. Illustrative examples are included to...

We study a dynamic model for viscoelastic materials based on a constitutive equation of fractional order. This results in an integrodifferential equation with a weakly singular convolution kernel. We discretize in the spatial variable by a standard Galerkin finite element method. We prove stability and regularity estimates which show how the convolution term introduces dissipation into the equa...

We introduce a one parameter family of non-linear, non-local integrodifferential equations and its limit equation. These equations originate from a derivation of the linear Boltzmann equation using the framework of bosonic quantum field theory. We show the existence and uniqueness of strong global solutions for these equations, and a result of uniform convergence on every compact interval of th...

In a previous article [1] we have shown how one can employ Artificial Neu-ral Networks (ANNs) in order to solve non-homogeneous ordinary and partial differential equations. In the present work we consider the solution of eigen-value problems for differential and integrodifferential operators, using ANNs. We start by considering the Schrödinger equation for the Morse potential that has an analyt...