In this paper, we consider Adomian Decomposition Method (ADM),and Variational Iteration Method (VIM), Homotopy Analysis Method (HAM), Homotopy Analysis Transform Method (HATM) to solve the FractionalOrder Logistic Equation (FOLE). Comparisons between the approximate analytical solution and exact solution of FOLE are shown. 2010 Mathematics Subject Classication: 34-XX , 34Lxx ,34L30

This paper presents the application of Homotopy Analysis Method (HAM) for solving nonlinear system Volterra integral equations used to obtain a reasonably approximate solution. The HAM contains auxiliary parameter h which provides simple way adjust and control convergence region solution series. results show that is very effective method as well. were compared with solutions obtained by develop...

One of the efficient and powerful schemes to solve linear and nonlinear equations is homotopy analysis method (HAM). In this work, we obtain the approximate solution of a system of partial differential equations (PDEs) by means of HAM. For this purpose, we develop the concept of HAM for a system of PDEs as a matrix form. Then, we prove the convergence theorem and apply the proposed method to fi...

The homotopy analysis method HAM is applied to obtain the approximate traveling wave solutions of the coupled Whitham-Broer-Kaup WBK equations in shallow water. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the systems of nonlinear partial differential equations.

In this paper, homotopy analysis method is presented for linear system of first-order fuzzy differential equations which involves a radioactivity decay model. We give the illustrative example to demonstrate the efficiency of the method. Finally, homotopy analysis method (HAM) is applied to obtain series solutions to the the radioactivity decay model.

In this study the application of a newly developed efficient method namely, optimal q-homotopy analysis method (Oq-HAM) has been illustrated for solving second order initial and boundary value problems. The Oq-HAM is a flexible method and can be applied to solve different types of problems. Moreover, it can easily be implemented in symbolic soft computing tools, e.g. MATHEMATICA.

Here, the homotopy analysis method (HAM), which is powerful tool for nonlinear problems, applied to solve the prey and predator problem. The homotopy analysis method contains the auxiliary parameter ¯ h, which provides us with a simple way to adjust and control convergence region of solution series.

In this paper we have used the homotopy analysis method (HAM) to obtain solution of space-time fractional advectiondispersion equation. The fractional derivative is described in the Caputo sense. Some illustrative examples have been presented. The obtained results using homotopy analysis method demonstrate the reliability and efficiency of the proposed algorithm.

Although perturbation techniques are widely applied to analyze nonlinear problems in science and engineering, they are however so strongly dependent on small parameters appeared in equations under consideration that they are restricted only to weakly nonlinear problems. For strongly nonlinear problems which don’t contain any small parameters, perturbation techniques are invalid. So, it seems ne...