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...

Presented herein is an analytical approach based on homotopy analysis method (HAM) used to deal with the seventh-order Duffing type problem with high-order nonlinearity. Such a problem corresponds to the large-amplitude vibration of an electrostatically actuated microbeam. Unlike tradition HAM, the convergence-control auxiliary parameters ( ) i i 1,2 m = ħ ⋯ are introduced in the present approx...

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...

An analytical technique, namely the homotopy analysis method (HAM), is applied to solve periodic solutions for superharmonic resonances of nonlinear oscillations with parametric excitation. Unlike perturbation methods, HAM does not depend on any small physical parameters at all. Thus, it is valid for both weakly and strongly nonlinear problems. Besides, different from all other analytic techniq...

In this paper, the mixed convection steady boundary layer stagnation point flow and heat transfer of a third grade fluid over an exponentially stretching sheet is investigated. Both the analytical and numerical solutions are carried out. The analytical solutions are obtained through the homotopy analysis method (HAM) while the numerical solutions are computed by using the Keller box method (K-b...

This study examines the simultaneous effects of heat and mass transfer on the three-dimensional boundary layer flow of viscous fluid between two infinite parallel plates. Magnetohydrodynamic (MHD) and thermal radiation effects are present. The governing problems are first modeled and then solved by homotopy analysis method (HAM). Influence of several embedded parameters on the velocity, concent...