Approximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform Method
Provides an analytical-numerical technique for solving a class of fractional PDEs, but the contribution is incremental as it applies an existing method to a known problem.
The paper applies the Fractional Reduced Differential Transform Method (FRDTM) to solve nonlinear fractional Klein-Gordon equations, obtaining convergent series solutions. The method is shown to be efficient and reliable compared to the Implicit Runge-Kutta approach.
This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Reduced Differential Transform Method (FRDTM). This technique provides the solutions very accurately and efficiently in convergent series formula with easily computable coefficients. The behavior of the approximate series solution for different values of fractional-order "a" is shown graphically. A comparative study is presented between the FRDTM and Implicit Runge-Kutta approach to illustrate the efficiency and reliability of the proposed technique. Our numerical investigations indicate that the FRDTM is simple, powerful mathematical tool and fully compatible with the complexity of such problems.