‎in this paper‎, ‎we formulate the sixth-order boundary value problem as fredholm integral equation by finding green's function and obtain the sufficient conditions for existence and multiplicity of positive solution for this problem‎. ‎also nonexistence results are obtained‎. ‎an example is given to illustrate the results of paper‎.

An analysis is presented of the torsional vibration of a rigid disc embedded to the surface of a transversely isotropic elastic half space. By using Hankel transform the mixed boundary value problem transform into a dual integral equation, which then transform to a Fredholm integral equation. After reduction to a Fredholm’s integral equation of second kind, solutions to the problem are obtained...

In this paper, continuous Legendre multi-wavelets are utilized as a basis in a practical direct method to approximate the solutions of the Fredholm integral equations system. To begin with we describe the characteristic of Legendre multi-wavelets and will go on to indicate that through this method a system of Fredholm integral equations can be reduced to an algebraic equation. Finally, numerica...

In this paper, we propose a successive approximation method based on fuzzy wavelet like operator to approximate the solution of linear fuzzy Fredholm integral equations of the second kind with arbitrary kernels. We give the convergence conditions and an error estimate. Also, we investigate the numerical stability of the computed values with respect to small perturbations in the first iteration....

One of the methods for solving definite integrals is modified trapezoid method, which is obtained by using Hermitian interpolation (see e.g. [12]). In this article, we have used modified trapezoid quadrature method and Generalized differential to solve the Fredholm fuzzy integral equations of the second kind. This method leads to solve fuzzy linear system. Finally the proposed method is illustr...

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...

We derive and analyze two equivalent integral formulations for the time-harmonic electromagnetic scattering by a dielectric object. One is a volume integral equation (VIE) with a strongly singular kernel and the other one is a coupled surface-volume system of integral equations with weakly singular kernels. The analysis of the coupled system is based on standard Fredholm integral equations, and...

an ecient method, based on the legendre wavelets, is proposed to solve thesecond kind fredholm and volterra integral equations of hammerstein type.the properties of legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known newton's method. examples assuring eciencyof the method and ...

The paper presents a method for constructing the characteristic equation of SISO linear periodic dynamical systems with distributed delay. The construction bases on a description in frequency domain, and a relation between the characteristic function of the periodic system and the Fredholm denominator of an associated Fredholm integral equation of the second kind. Using the Fredholm calculus, p...