This work proposes an interval-based uncertain Susceptible–Infected–Recovered (SIR) epidemic model. The interval model has been numerically solved by the homotopy analysis method (HAM). SIR is proposed and under different intervals HAM to obtain numerical solution of Furthermore, ODE was transformed into a stochastic differential equation (SDE) results deterministic models were compared using s...

The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourthorder differential equation by using similarity solutions. Homotopy analysis method HAM is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefu...

We consider the application of a new analytic method based on homotopy analysis to the solution of the steady flow of a viscous incompressible fluid past a fixed circular cylinder. The solutions obtained using this method produce some interesting results. For instance, an analytic verification of the critical Reynolds number Rd for which a standing vortex first appears behind the cylinder is gi...

In the present paper, we have focused our attention to highlight the study of a non-Newtonian nanofluid between coaxial cylinders with variable viscosity. The governing equations of the nonNewtonian fluid with variable viscosity along with energy and nanoparticles are given. The coupled nonlinear differential equations are solved analytically with the help of the homotopy analysis method (HAM)....

Based on the homotopy analysis method (HAM), we propose an analytical approach for solving the following type of nonlinear boundary value problems in finite domain. In framework of HAM a convenient way to adjust and control the convergence region and rate of convergence of the obtained series solutions, by defining the so-called control parameter , is provided. This paper aims to propose an eff...

In this paper, the nonlinear free vibrations of thin symmetric and non-symmetric cross-ply composite plates subjected to biaxial initial stresses are investigated. Because of their excellent properties such as specific strength and specific stiffness, composite plates have wide applications in aerospace and mechanical structures. Based on Von-Karman's strain-displacement relations and using Gal...

In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...

This paper focuses on the usage of homotopy analysis method (HAM) to solve fractional heat conduction equation. In presented mathematical model, Caputo-type derivatives over time or space are considered. HAM, it is not necessary discretize considered domain, which its great advantage. As a result method, continuous function obtained, can be used for further analysis. For first time, equations, ...

The magnetohydrodynamic (MHD) flow of third grade nanofluid between coaxial porous cylinders was investigated in this work. Two types of series solutions were presented for constant and variable viscosity. The resulting nonlinear coupled equations were solved by employing homotopy analysis method (HAM). The convergence of the series solutions has been discussed explicitly. The recurrence formul...

Received 19 May 2010; received in revised 30 October 2011; accepted 18 January 2012 ABSTRACT This paper considers an important model of boundary value problem with a condition at infinity namely combined free and forced convection over a plane of arbitrary shape embedded in a fluid-saturated porous medium; this model admits dual solutions, and uses a technique, which is to some extent modificat...