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In this paper, we develop a method to calculate numerical and approximate solution of some fifth-order Korteweg-de Vries equations with initial condition with the help of Laplace Decomposition Method (LDM). The technique is based on the application of Laplace transform to some fifth-order Kdv equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this technique with the help of four examples and results of the present technique have closed agreement with approximate solutions obtained with the help of (LDM).

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I.

In this paper we prove the existence of solution of coupled system of quadratic hybrid functional integral equations. Our main result is based on the standard tools of fixed point theory. The Existence and locally attractivity is proved ℛ + .