Here, the solution in one, two and three dimensional for the Volterra–Fredholm integral equation of the first kind is obtained in the space L2ðXÞ C1⁄20; T , T < 1. Using a numerical method the integral equation of Volterra–Fredholm becomes a linear system of Fredholm integral equation when that the kernel of Fredholm integral takes a logarithmic form, Carleman function, generalized potential fu...

In this paper, we study the approximate solution of two-dimensional nonlinear Volterra integral equations by two-dimensional differential transform method. New theorems for the transformation of integrals are introduced and proved. We will give an applicable relation between the two-dimensional nonlinear Volterra integral equations and two-dimensional differential transformation, in order to so...

Algorithms for the symbolic computation of polynomial conserved densities, fluxes, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations are presented. In the algorithms we use discrete versions of the Fréchet and variational derivatives, as well as discrete Euler and homotopy operators. The algorithms are illustrated for prototypical nonline...

This paper exhibits an algorithm based on Volterra-type processing in order to detect several independent sources on the same carrier frequency and to determine the number of them. The use of infinite impulse ratio (IIR) Volterra filtering to build a suitable discrimination test is dictated by the need of higher-order moments in this type of nonlinear problem, as well as the need of IIR for con...

The discrete variational identity under general bilinear forms on semi-direct sums of Lie algebras is established. The constant γ involved in the variational identity is determined through the corresponding solution to the stationary discrete zero curvature equation. An application of the resulting variational identity to a class of semi-direct sums of Lie algebras in the Volterra lattice case ...

Some existence and uniqueness theorems are established for weakly singular Volterra and Fredholm-Volterra integral equations in C[a, b]. Our method is based on fixed point theorems which are applied to the iterated operator and we apply the fiber Picard operator theorem to establish differentiability with respect to parameter. This method can be applied only for linear equations because otherwi...

Email: [email protected] Abstract: In this study, we contribute to the existing theory of abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces. We investigate a class of abstract degenerate Volterra inclusions by using the multivalued linear operator approach, as well as a class of abstract degenerate multi-term fractional differential equat...

We formulate and analyze a new method for solving optimal control problems for systems governed by Volterra integral equations. Our method utilizes discretization of the original Volterra controlled system and a novel type of dynamic programming jn which the Hamilton-Jacobi function is parametrized by the control function (rather than the state, as in the case of ordinary dynamic programming). ...

Rationalized Haar functions are developed to approximate the solution of the nonlinear Volterra–Fredholm–Hammerstein integral equations. The properties of rationalized Haar functions are first presented. These properties together with the Newton–Cotes nodes and Newton–Cotes integration method are then utilized to reduce the solution of Volterra–Fredholm–Hammerstein integral equations to the sol...

Using Schaefer’s fixed-point theorem, enabling us to show that if there is an a priori bound on all possible T -periodic solutions of an infinite delay Volterra difference equation, then there is a T -periodic solution. We apply our results to scalar infinite delay Volterra difference equations in which, the a priori bound is established by means of nonnegative definite Lyapunov functionals. AM...