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Solving nonlinear fractional partial differential equations using the homotopy analysis method
Author(s) -
Dehghan Mehdi,
Manafian Jalil,
Saadatmandi Abbas
Publication year - 2010
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20460
Subject(s) - mathematics , homotopy analysis method , partial differential equation , nonlinear system , korteweg–de vries equation , partial derivative , fractional calculus , integer (computer science) , mathematical analysis , homotopy , method of characteristics , first order partial differential equation , pure mathematics , physics , quantum mechanics , computer science , programming language
In this article, the homotopy analysis method is applied to solve nonlinear fractional partial differential equations. On the basis of the homotopy analysis method, a scheme is developed to obtain the approximate solution of the fractional KdV, K (2,2), Burgers, BBM‐Burgers, cubic Boussinesq, coupled KdV, and Boussinesq‐like B ( m , n ) equations with initial conditions, which are introduced by replacing some integer‐order time derivatives by fractional derivatives. The homotopy analysis method for partial differential equations of integer‐order is directly extended to derive explicit and numerical solutions of the fractional partial differential equations. The solutions of the studied models are calculated in the form of convergent series with easily computable components. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010