Exact Solutions of the Nonlinear Space-Time Fractional Partial Differential Symmetric Regularized Long Wave (SRLW) Equation by Employing Two Methods
Qinghao Zhu, Jianming Qi
Abstract
In this article, with the aid of Maple software, the exact solutions to the space-time fractional symmetric regularized long wave (SRLW) equation are successfully examined by <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mfenced open="(" close=")"> <a:mrow> <a:msup> <a:mrow> <a:mi>G</a:mi> </a:mrow> <a:mrow> <a:mo>′</a:mo> </a:mrow> </a:msup> <a:mo>/</a:mo> <a:msup> <a:mrow> <a:mi>G</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:msup> </a:mrow> </a:mfenced> </a:math> -expansion and extended complex methods. Consequently, three types of traveling wave solutions are found such as Weierstrass double periodic elliptic functions, simply periodic functions, and the rational function solutions. The obtained results will play an important role in understanding and studying SRLW equation. It is easy to see that the extended complex and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M2"> <e:mfenced open="(" close=")"> <e:mrow> <e:msup> <e:mrow> <e:mi>G</e:mi> </e:mrow> <e:mrow> <e:mo>′</e:mo> </e:mrow> </e:msup> <e:mo>/</e:mo> <e:msup> <e:mrow> <e:mi>G</e:mi> </e:mrow> <e:mrow> <e:mn>2</e:mn> </e:mrow> </e:msup> </e:mrow> </e:mfenced> </e:math> -expansion methods are reliable and will be used extensively to seek exact solutions of any other fractional nonlinear partial differential equations (FNPDE).