Approximate Series Solution of Nonlinear, Time Fractional- order Klein-Gordon Equations Using Fractional Reduced Differential Transform Method (original) (raw)
The main goal of this paper is to present a new approximate series solution of the one-dimensional, nonlinear Klein-Gordon equations with time-fractional derivative in Caputo form using a recently semi-analytical technique, called fractional reduced differential transform method (FRDTM). This technique provides the solutions very accurately and efficiently in the form of convergent series with easily computable components. The behavior of the approximate series solution for different values of fractional-order is shown graphically. A comparative study is presented between FRDTM and the Implicit Runge-Kutta method, in the case of integer-order derivative, to demonstrate the validity and applicability of the proposed technique. The results reveal that the FRDTM is a very simple, straightforward and powerful mathematical tool for a wide range of real-world phenomena arising in engineering, biology and physical sciences that modelled in terms of fractional differential equations.
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