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

## TL;DR

This paper introduces the Fractional Reduced Differential Transform Method (FRDTM) for efficiently solving nonlinear fractional Klein-Gordon equations, demonstrating high accuracy and convergence through graphical and comparative analyses.

## Contribution

The paper presents a novel application of FRDTM to nonlinear fractional Klein-Gordon equations, providing an accurate, efficient, and easily computable series solution method.

## Key findings

- FRDTM yields highly accurate solutions
- The method converges rapidly for different fractional orders
- Comparison shows FRDTM outperforms Implicit Runge-Kutta in efficiency

## Abstract

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.

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Source: https://tomesphere.com/paper/1704.06982