In this paper, He’s homotopy perturbation method (HPM) is applied to spatial one and three spatial dimensional inhomogeneous wave equation Cauchy problems for obtaining exact solutions. HPM is used for analytic handling of these equations. The results reveal that the HPM is a very effective, convenient and quite accurate to such types of partial differential equations (PDEs). Keywords—Homotopy ...

‎ in this paper, we investigate stability analysis of fractional differential systems equipped with the conformable fractional derivatives. some stability conditions of fractional differential systems are proposed by applying the fractional exponential function and the fractional laplace transform. moreover, we check the stability of conformable fractional lotka-volterra system with the multi-st...

In this paper, we apply Homotopy Analysis Transform Method (HATM) for solving various nonlinear equations. This method is the combined for of the homotopy analysis method and Laplace transform method. HATM is applied without any discretization or restrictive assumption and avoids roundoff errors which may lead the solution in closed form. The results reveal that the HATM is very effective, conv...

As an effective method for solving linear and nonlinear equations, the homotopy perturbation is usually applied to relevant problems. We analyze 74 studies on application of present a comprehensive review them with conclusion obtained: (1) Homotopy generally problems ordinary differential equations; (2) combined technology transform when it used solve more complicated (3) By comparing other sim...

in this paper, the homotopy perturbation method (hpm) is applied to obtain an approximate solution of the fractional bratu-type equations. the convergence of the method is also studied. the fractional derivatives are described in the modied riemann-liouville sense. the results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional...

The aim of this work is to apply the homotopy perturbation method and homotopy analysis method to the problem of thermal explosion in a flammable gas mixture with the addition of volatile fuel droplets. The system of equations that describes the effects of heating, evaporation, and combustion of fuel in a polydisperse spray is simplified. Both convective and radiative heating of droplets is tak...

In this paper, He’s homotopy perturbation method (HPM) is applied for solving linear programming (LP) problems. This paper shows that some recent findings about this topic cannot be applied for all cases. Furthermore, we provide the correct application of HPM for LP problems. The proposed method has a simple and graceful structure. Finally, a numerical example is displayed to illustrate the pro...