TY - JOUR
T1 - Solving the fractional nonlinear Klein-Gordon equation by means of the homotopy analysis method
AU - Kurulay, Muhammet
PY - 2012
Y1 - 2012
N2 - In this paper, the homotopy analysis method is applied to obtain the solution of nonlinear fractional partial differential equations. The method has been successively provided for finding approximate analytical solutions of the fractional nonlinear Klein-Gordon equation. Different from all other analytic methods, it provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter ħ. The analysis is accompanied by numerical examples. The algorithm described in this paper is expected to be further employed to solve similar nonlinear problems in fractional calculus.
AB - In this paper, the homotopy analysis method is applied to obtain the solution of nonlinear fractional partial differential equations. The method has been successively provided for finding approximate analytical solutions of the fractional nonlinear Klein-Gordon equation. Different from all other analytic methods, it provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter ħ. The analysis is accompanied by numerical examples. The algorithm described in this paper is expected to be further employed to solve similar nonlinear problems in fractional calculus.
KW - analytical solutions
KW - fractional nonlinear Klein-Gordon equations
KW - homotopy analysis method
UR - http://www.scopus.com/inward/record.url?scp=84873401814&partnerID=8YFLogxK
U2 - 10.1186/1687-1847-2012-187
DO - 10.1186/1687-1847-2012-187
M3 - Article
AN - SCOPUS:84873401814
SN - 1687-1839
VL - 2012
JO - Advances in Difference Equations
JF - Advances in Difference Equations
M1 - 187
ER -