Solving the fractional nonlinear Klein-Gordon equation by means of the homotopy analysis method - Kurulay, Muhammet (SPRINGEROPEN, 2012)
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 (h) over bar. 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.
Keywords: fractional nonlinear Klein-Gordon equations; homotopy analysis method; analytical solutions; PARTIAL-DIFFERENTIAL-EQUATIONS; APPROXIMATE SOLUTION TECHNIQUE; SMALL PARAMETERS; Mathematics