asymptotically exact and nonlocal fourth order nonlinear evolution equations are derived for two coupled fourth order nonlinear evolution equations have been derived in deep water for two capillary-gravity wave packets propagating in the same direction in the presence of wind flowing over water.we have used a general method, based on zakharov integral equation.on the basis of these evolution eq...

 In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an IVP of first order hybrid  random differential equations with the linear perturbation of second type. A comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential eq...

In this article, we give some results concerning the continuity of the nonlinear Volterra and Fredholm integral operators on the space L1[0,∞). Then by using the concept of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes of nonlinear integral equations. Our results extend some previous works.

Most of the methods, which used to solve nonlinear integral equations, transform the equation into a system of nonlinear equations. It is cumbersome to solve these systems, or the solution may be unreliable. In this paper, we propose an iterative approach based on fixed point method and Sinc quadrature, which has exponentially rate of convergence, to solve Hammerstein integral equation. Converg...

An approximation method based on operational matrices of Bernstein polynomials used for the solution of Hammerstein integral equations. The operational matrices of these functions are utilized to reduce a nonlinear Hammerstein and Volterra Hammerstein integral equation to a system of nonlinear algebraic equations. The method is computationally very simple and attractive, and applications are de...