In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In this paper a novel approach based on the homotopy analysis method (HAM) is presented for solving nonlinea...

although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.here, after criticizi...

A modification of the homotopy analysis method (HAM) for solving a system of nonlinear boundary value problems (BVPs) in semi–infinite domain, micropolar flow due to a linearly stretching of porous sheet, is proposed. This method is based on operational matrix of exponential Chebyshev functions to construct the derivative and product of the unknown function in the matrix form. In addition, by u...

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 present a new approach for finding periodic orbits in dynamical systems modeled by differential equations. It is based on the Homotopy Analysis Method (HAM) but it differs from the usual way it is applied. We apply the HAM to construct approximations of a formal series solution of the equation. These approximations exist for any value of the frequency. They can be obtained by c...

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...

Many of nonlinear systems in the field of engineering such as nano-resonator and atomic force microscope can be modeled based on Duffing equation. Analytical frequency response of this system helps us analyze different interesting nonlinear behaviors appearing in its response due to its rich dynamics. In this paper, the general form of Duffing equation with cubic nonlinearity as well as par...

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...