Approximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform Method

摘要

This analysis proposes an analytical-numerical approach for providingsolutions of a class of nonlinear fractional Klein-Gordon equation subjected toappropriate initial conditions in Caputo sense by using the Fractional ReducedDifferential Transform Method (FRDTM). This technique provides the solutionsvery accurately and efficiently in convergent series formula with easilycomputable coefficients. The behavior of the approximate series solution fordifferent values of fractional-order "a" is shown graphically. A comparativestudy is presented between the FRDTM and Implicit Runge-Kutta approach toillustrate the efficiency and reliability of the proposed technique. Ournumerical investigations indicate that the FRDTM is simple, powerfulmathematical tool and fully compatible with the complexity of such problems.