In this paper, we apply the homotopy perturbation method (HPM), modified method(MHPM), variational iteration (VIM), Adomian decomposition (ADM), and (MADM) to solve nonlinear mixed Volterra-Fredholm integral equations itssystem. We investigate approximate solution of equation its system via proposed methods. Thevalidity efficiency these methods are demonstrated through various numerical example...

In this paper, Homotopy Analysis Method is used to analyze free non-linear vibrations of a beam simply supported by pinned ends under axial force. Mid-plane stretching is also considered for dynamic equation extracted for the beam. Galerkin decomposition technique is used to transform a partial dimensionless nonlinear differential equation of dynamic motion into an ordinary nonlinear differenti...

In this paper, we apply the  homotopy analysis method (HAM) for solving fuzzy  linear systems and present  the necessary and sufficient conditions for the convergence of series solution obtained via the HAM. Also, we present a new criterion for choosing a proper value of convergence-control parameter $hbar$ when the HAM is applied to linear system of equations. Comparisons are made between the ...

In this article, we use the homotopy perturbation transform method to find fractional Kersten–Krasil’shchik coupled Korteweg–de Vries (KdV) non-linear system. This system is typically used describe electric circuits, traffic flow, shallow water waves, elastic media, electrodynamics, etc. The modified with help of ρ-Laplace transformation investigate solution given examples show accuracy current...