Abstract
In this article, the ( G ′ / G ) -expansion method is used for the analytical solutions of fractional-order Klein-Gordon and Gas Dynamics equations. The fractional derivatives are defined in the term of Jumarie’s operator. The proposed method is based on certain variable transformation, which transforms the given problems into ordinary differential equations. The solution of resultant ordinary differential equation can be expressed by a polynomial in ( G ′ / G ) , where G = G ( ξ ) satisfies a second order linear ordinary differential equation. In this paper, ( G ′ / G ) -expansion method will represent, the travelling wave solutions of fractional-order Klein-Gordon and Gas Dynamics equations in the term of trigonometric, hyperbolic and rational functions.
Highlights
The aim of the present paper is to solve the fractional-order a Klein-Gordon and Gas Dynamics equations
The ( G /G )-expansion method is applied for the analytical solutions of fractional Klein-Gordon and Gas Dynamics equations
The ( G /G )-expansion method is implemented in series form with some unknown coefficients, which provide the system of algebraic equations containing these unknowns
Summary
The aim of the present paper is to solve the fractional-order a Klein-Gordon and Gas Dynamics equations. Most engineering and physical phenomena are modeled correctly by using fractional. The FDEs have many applications in science and engineering such as earthquake model [4], signal control system [5], wave models [6], finance models [7] and so on. Most of the researchers have presented various techniques for the solutions of FDEs, fractional Partial Differential Equations (FPDEs) is the point of interest. Among the FPDEs, the Klein-Gordon model is one of the mathematical models in quantum field theory. This model appears in non-linear optics, plasma physics, relativistic physics and describe dispersive wave phenomena. The variety of some other physical phenomena such as ferromagnetic and ferroelectric domain walls, DNA dynamics and Josephson and dislocation junctions are described well by KG model [8]
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