In this study, we present a new general solution to rational epidemiological mathematical model via recent intelligent method called the natural transform homotopy analysis (NTHAM), which combines two methods: (NTM) and (HAM). To assess precision reliability of method, compared obtained results with those Laplace perturbation (LHPM) as well q-homotopy Sumudu (q-HASTM), revealed that NTHAM is mo...

In this paper the problem of Kirchhoff simplified model for beam is studied and analytical solution is presented. Governing equation is solved analytically using a kind of analytic technique for nonlinear problems namely the Homotopy Analysis Method (HAM), for the first time. Present solution gives an expression which can be used in wide range of time for all domain of response and method is ab...

In this paper we examine fluctuation and frequency of the governing equation ofoscillator with odd and even nonlinearities without damping and we present a new efficientmodification of the He’s homotopy perturbation method for this equation. We applied standard andmodified homotopy perturbation method and compare them with the numerical solution (NS), also weapplied He’s Energy balance method (...

Childhood vaccination programs have had a dramatic impact on child morbidity and mortality. Protecting children from diseases that can be prevented by vaccination is a primary goal of health administrators. A SIR model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine is presented in this paper. We introduce fractional-order into the presented mode...

In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtainedusing theHomotopyAnalysisMethod (HAM) andHomotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results andnumerical solutions shows that only the first order approximation of the Homotopy ...

The analytical solution of the Initial Value Problem (IVP) and Boundary (BVP) is an essential issue in numerous engineering applications. However, it cannot usually be realized by simple methods. Accordingly, utilizing semi-analytical methods such as homotopy analysis method (HAM) alternative. depends on calculating a dedicated convergence parameter. Different algorithms were proposed to realiz...

This work is concerned with the series solutions for the flow of third-grade non-Newtonian fluid with variable viscosity. Due to the nonlinear, coupled, and highly complicated nature of partial differential equations, finding an analytical solution is not an easy task. The homotopy analysis method HAM is employed for the presentation of series solutions. The HAM is accepted as an elegant tool f...

A non-Darcy flow with moving boundary conditions in a low-permeability reservoir was solved using the homotopy analysis method (HAM), which converted into fixed-boundary mathematical model via similarity transformation. Approximate analytical solutions based on HAM are guaranteed to be more accurate than exact solutions, relative errors between 0.0089% and 2.64%. When λ = 0, pressure drop of Da...

mhd boundary layer flow of two phase model nanofluid over a vertical plate is investigated both analytically and numerically. a system of governing nonlinear partial differential equations is converted into a set of nonlinear ordinary differential equations by suitable similarity transformations and then solved analytically using homotopy analysis method and numerically by the fourth order rung...

Squeezing flow of a Casson fluid is considered between two parallel disks. Upper disk is taken to be impermeable but capable of moving towards or away from the lower fixed and porous disk. Governing equations are derived with the help of conservation laws combined with suitable similarity transforms. Homotopy analysis method (HAM) is then been employed to determine the solution to resulting ord...