Slodička, Marian
Published in
Inverse Problems

This paper deals with direct and inverse source problems for parabolic or byperbolic PDEs containing nonlinear Volterra operators (including the variable order time-fractional derivatives). We show the well posedness (existence and uniqueness of a solution) of various settings. The proof-technique is based on the contraction mapping theorem and on ...

Kurganov, K. A. Jamilov, U. U. Okhunova, M. O.
Published in
Lobachevskii Journal of Mathematics

AbstractIn present paper we consider a family of discrete time Kolmogorov systems of three interaction population depending on a parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...

Jamilov, U. U. Kurganov, K. A.
Published in
Lobachevskii Journal of Mathematics

AbstractIn the present paper we consider a family of non-Volterra cubic stochastic operators depending on a parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\t...

Jamilov, U. U.
Published in
Mathematical Notes

Vlasov, V. V. Rautian, N. A.
Published in
Doklady Mathematics

AbstractIntegro-differential equations with unbounded operator coefficients in a Hilbert space are studied. The equations under consideration are abstract hyperbolic equations perturbed by terms containing Volterra integral operators. These equations are operator models of integro-differential equations with partial derivatives arising in the theor...

Khadkhuu, Lkhamjav Tsedenbayar, Dashdondog
Published in
Mathematica Slovaca

Let V denote the classical Volterra operator on L2[0,1] and let z1,z2 be arbitrary complex numbers. We investigated the operator norm of z1V+z2V*$ z_{1}V+z_{2}V^{*} $.

Zakovorotny, V. L. Lapshin, V. P. Babenko, T. S.
Published in
Russian Engineering Research

Modeling of the wear at the rear tool face in the turning of metals is based on an integral Volterra operator of the second kind. That permits adequate formal representation of tool wear in terms of the work and the power of irreversible energy transformations in the cutting zone.

Abu Arqub, Omar Rashaideh, Hasan
Published in
Neural Computing and Applications

Many problems arising in different fields of sciences and engineering can be reduced, by applying some appropriate discretization, either to a system of integrodifferential algebraic equations or to a sequence of such systems. The aim of the present analysis is to implement a relatively recent computational method, reproducing kernel Hilbert space,...

Al Alam, Ihab Habib, Georges Lefèvre, Pascal Maalouf, Fares

We study the properties of the Volterra and Cesàro operators viewed on the L 1-Müntz space with range in the space of continuous functions. These operators are neither compact nor weakly compact. We estimate how far from being (weakly) compact they are by computing their (generalized) essential norm. It turns out that this latter does not depend on...

Parisini, T Pin, G Chen, B

A novel finite-time convergent estimation technique is prop osed for identifying the amplitude, frequency and phase of a biased sinusoidal signal. Resorting to Volterra integral operato rs with suitably designed kernels, the measured signal is pr ocessed yielding a set of auxiliary signals in which the influence of t he unknown initial conditions i...