| Summary: | In this article, the <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <msup> <mi>G</mi> <msup> <mrow></mrow> <mo>′</mo> </msup> </msup> <mo>/</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>-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 <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <msup> <mi>G</mi> <msup> <mrow></mrow> <mo>′</mo> </msup> </msup> <mo>/</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>, where <inline-formula> <math display="inline"> <semantics> <mrow> <mi>G</mi> <mo>=</mo> <mi>G</mi> <mo stretchy="false">(</mo> <mo>ξ</mo> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula> satisfies a second order linear ordinary differential equation. In this paper, <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <msup> <mi>G</mi> <msup> <mrow></mrow> <mo>′</mo> </msup> </msup> <mo>/</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>-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.
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