A Taylor matrix method is developed to find an approximate solution of the most general linear Fredholm integrodifferential-difference equations with variable coefficients under the mixed conditions in terms of Taylor polynomials. This method transforms the given general linear Fredholm integrodifferential-difference equations and the mixed conditions to matrix equations with unknown Taylor coe...

T The nonlinear and linear Volterra-Fredholm ordinary integral equations arise from various physical and biological models. The essential features of these models are of wide applicable. These models provide an important tool for modeling a numerous problems in engineering and science [6, 7]. Modelling of certain physical phenomena and engineering problems [8, 9, 10, 11, 12] leads to two-dimens...

In this article we consider examples of Fredholm modules over the group C*-algebras of the infinite dihedral and discrete Heisenberg groups. In the first case we exhibit sufficient Fredholm modules to generate the entire K-homology of the algebra. We then turn our attention to the six term cyclic exact sequence in K-homology for a crossed product by Z dual to the Pimsner-Voiculescu sequence for...

Fredholm Alternative is a classical tool of periodic linear equations, allowing to describe the existence of periodic solutions of an inhomogeneous equation in terms of the adjoint equation. A few partial extensions have been proposed in the literature for recurrent equations: our aim is to point out they have a common root and discuss whether such root gives rise to a general Fredholm–type Alt...

In this paper we are concerned with highaccuracy quadrature method solutions of nonlinear Fredholm integral equations of the form

In [1], by using Fredholm index we developed a version of Quillen’s geometric cobordism theory for infinite dimensional Hilbert manifolds. This cobordism theory has a graded group structure under topological union operation and has push-forward maps for complex orientable Fredholm maps. In [19], by using Quinn’s Transversality Theorem [23], it has been shown that this cobordism theory has a gra...

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...