Finance

Klein–Gordon equation

Gene

Physics

Mathematical analysis

Linear differential equation

Fractional calculus

Repressor

Nonlinear system

Economics

Operator (biology)

Trigonometric functions

Order (exchange)

Chemistry

Geometry

Trigonometry

Traveling wave

Mathematics

Ordinary differential equation

Biochemistry

Term (time)

Quantum mechanics

Rational function

Differential equation

Transcription factor

Polynomial

Hyperbolic function

Partial differential equation

Symmetry

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.

Analytical Solutions of Fractional Klein-Gordon and Gas Dynamics Equations, via the (G′/G)-Expansion Method