Solving Fractional Fornberg-whitham Equation by Homotopy Analysis Method
نویسندگان
چکیده
In this paper, The analytical solution of the nonlinear Fornberg-Whitham equation with fractional time derivative was derived by means of the homotopy analysis method. The fractional derivatives are described in the Caputo sense. By choosing different values of the parameters in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained. The results reveal that the proposed method is very effective and simple for solving approximate solutions. Mathematics Subject Classification 2000: MSC2010 database 65Z05 , , General Terms: Documentation, Languages Additional
منابع مشابه
Application of new iterative transform method and modified fractional homotopy analysis transform method for fractional Fornberg-Whitham equation
The main purpose of this paper is to present a new iterative transform method (NITM) and a modified fractional homotopy analysis transform method (MFHATM) for time-fractional Fornberg-Whitham equation. The numerical results show that the MFHATM and NITM are very efficient and highly accurate for nonlinear fractional differential equations. c ©2016 All rights reserved.
متن کاملAnalytical Approximate Solution For Nonlinear Time-Space Fractional Fornberg-Whitham Equation By Fractional Complex Transform
In this article, fractional complex transform with optimal homotopy analysis method (OHAM) is used to obtain numerical and analytical solutions for the nonlinear time-space fractional Fornberg-Whitham. Fractional complex transform is proposed to convert time-space fractional Fornberg-Whitham equation to the nonlinear ordinary differential equations and then applied OHAM to the new obtained equa...
متن کاملNon Probabilistic Solution of Fuzzy Fractional Fornberg-Whitham Equation
Fractional Fornberg-Whitham equation has a vast application in physics. There exist various investigations for the above problem by considering the variables and parameters as crisp/exact. In practice, we may not have these parameters exactly but those may be known in some uncertain form. In the present paper, these uncertainties are taken as interval/fuzzy and the authors proposed here a new m...
متن کاملNew Iterative Method for Solving the Fornberg-Whitham Equation and Comparison with Homotopy Perturbation Transform Method
This paper presents an approximate analytical solution of the nonlinear Fornberg-Whitham equation using the new iterative method (NIM). A comparison is made between the NIM results, homotopy perturbation transform method (HPTM) and the Adomian's decomposition method (ADM). The solution procedure reveals that NIM is a reliable, simple and effective. The proposed technique solves nonlinear proble...
متن کاملHomotopy perturbation method for solving fractional Bratu-type equation
In this paper, the homotopy perturbation method (HPM) is applied to obtain an approximate solution of the fractional Bratu-type equations. The convergence of the method is also studied. The fractional derivatives are described in the modied Riemann-Liouville sense. The results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional p...
متن کامل