The homotopy analysis method (HAM) is sharpened to solve the Thomas–Fermi equation. Some techniques are employed, including the use of asymptotic analysis to introduce proper transformation, and the use of optimal initial guess and optimal auxiliary linear operator to accelerate the convergence of homotopy approximations. The optimal convergence control parameters are determined by the minimum ...

The aim of this study is the investigation of the large amplitude deflection of an Euler-Bernoulli beam subjected to an axial load on a viscoelastic foundation with the strong damping. In order to achieve this purpose, the beam nonlinear frequency has been calculated by homotopy perturbation method (HPM) and Hamilton Approach (HA) and it was compared by the exact solutions for the different bou...

Abstract— In this paper, we have applied an accurate and efficient homotopy analysis method (HAM) to find the approximate/analytical solutions for space and time fractional reactiondiffusion equations arising in mathematical chemistry. The method provides solutions in rapid convergence series with computable terms. To the best of our knowledge, until now there is no rigorous HAM solutions have ...

In this paper, the basic ideas of a new kind of analytical technique, namely the Homotopy Analysis Method (HAM), are briefly described. Different from perturbation techniques, the HAM does not depend on whether or not there exist small parameters in nonlinear equations under consideration. Therefore, it provides us with a powerful tool to analyse strongly nonlinear problems. A simple but typica...

In this study, the concept of Homotopy analysis method (HAM) is briefly introduced. Furthermore some non-linear problems are handled and the solutions of these problems are given using by HAM, DTM, ADM methods and the convergence of the solution is shown to the exact solution. Additionally, the three methods are compared and it is observed that the HAM is more-less efficient and effective than ...

The homotopy analysis method HAM is employed to propose an approach for solving the nonlinear dynamical system of an electrostatically actuated micro-cantilever in MEMS. There are two relative merits of the presented HAM compared with some usual procedures of the HAM. First, a new auxiliary linear operator is constructed. This operator makes it unnecessary to eliminate any secular terms. Furthe...

In this paper, we applied the homotopy analysis method (HAM) to construct the analytical solutions of the space fractional diffusion equations. The derivatives are defined in the Jumarie’s fractional derivative sense. The explicit solutions of the equations have been presented in the closed form by using initial conditions. Two typical examples have been discussed. The results reveal that the m...

Abstract In this paper, we use new parametic formof fuzzy numbers and convert a system of fuzzy integral equations to two system of integral equations in crisp. Then we solve a system of fuzzy integral equations by means of an analytic technique, namely the homotopy analysis method (HAM). Using the HAM, it is possible to find the exact solution or an approximate solution of the problem. The res...

The paper must have abstract. In this paper, we present an approximate analytical algorithm to solve non-linear quadratic Riccati differential equations of fractional order based on the optimal homotopy asymptotic method (OHAM). OHAM has the benefit of adjusting the convergence rate and the region of the solution series via several auxiliary parameters over the homotopy analysis method (HAM) th...

Modeling infectious diseases helped out to understand and overcome epidemics. This paper is based on epidemic model SIR, which fits well to many epidemiological diseases. Basic idea of Homotopy Analysis Method (HAM)is discussed and employed to compute an approximation to the solution of nonlinear system of differential equations. The effect of vaccination on the dynamics of childhood disease de...