This paper reflects the implementation of a reliable technique which is called $left(frac{G'}{G}right)$-expansion  ethod for  constructing exact travelling wave solutions of nonlinear partial  differential equations. The proposed algorithm has been successfully tested on two two selected equations, the balance numbers of which are not positive integers namely Kundu-Eckhaus equation and  Derivat...

Nowadays, atomic force microscope is considered as a useful tool in the determination of intermolecular forces and surface topography with the resolution of nanometers. In this kind of microscope, micro cantilever is considered as the heart of the microscope and is used as a measuring tool.  This paper is aimed towards investigating the behavior of a piezoelectric micro cantilever with a triang...

Elzaki transform and Adomian polynomial is used to obtain the exact solutions of nonlinear fifth order Korteweg-de Vries (KdV) equations. In order to investigate the effectiveness of the method, three fifth order KdV equations were considered. Adomian polynomial is introduced as an essential tool to linearize all the nonlinear terms in any given equation because Elzaki transform cannot handle n...

In this paper, differential transform method (DTM) is described and is applied to solve systems of nonlinear ordinary differential equations which is arising in HIV infections of cell. Intervals of validity of the solution will be extended by using Pade approximation. The results also will be compared with those results obtained by Runge-Kutta method. The technique is described and is illustrat...

The major aim of this article is modeling of nonlinear systems with friction structure that, thismethod is essentially extended based on taylore expansion polynomial. So in this study, thetaylore expansion was extended in the generalized form for the differential equations of the statespaceform. The proposed structure is based on multi independent variables taylore extended.According to the pro...

an analysis is carried out to investigate the effects of variable chemical reaction, thermophoresis, temperaturedependent viscosity and thermal radiation on an unsteady mhd free convective heat and mass transfer flow of a viscous, incompressible, electrically conducting fluid past an impulsively started infinite inclined porous plate by taking into account the viscous dissipation effects. the g...

in this paper lie’s formalism is applied to deduce classes of solutions of a nonlinear partialdifferential equation (npde) of second order with quadratic nonlinearity. the equation has themeaning of a field equation appearing in the formulation of kinetic models. similaritysolutions and transformations are given in a most general form derived to the first time interms of reciprocal jacobian ell...

In this paper, the boundary layer flow of an Eyring-Powell non-Newtonian fluid over a linearly stretching sheet is solved using the combination of the quasilinearization method and the Fractional order of Rational Chebyshev function (FRC) collocation method on a semi-infinite domain. The quasilinearization method converts the equation into a sequence of linear equations then, using the FRC coll...

degenerate kernel approximation method is generalized to solve hammerstein system of fredholm integral equations of the second kind. this method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. convergence analysis is investigated and on some test problems, the propo...