A comparative analysis of generalized and extended (G'/G)-Expansion methods for travelling wave solutions of fractional Maccari's system with complex structure

Fractional partial differential equations emerge as a prominent research area in recent times owing to their ability to depict intricate physical phenomena. Discovering travelling wave solutions for fractional partial differential equations is an arduous task, and several mathematical approaches devise to address this issue. This investigation aims to compare two distinguished methods, namely, the generalized ( ������������ & PRIME;)-Expansion and the extended ( ������������ & PRIME;)-Expansion, in discovering the most optimal travelling wave solutions for fractional partial differential equations. Our observations indicate that the generalized ( ������������ & PRIME;)-Expansion method surpasses the extended ( ������������& PRIME; )-Expansion method regarding the count of travelling wave solutions obtained. Moreover, the generalized (������������ & PRIME; )-Expansion method furnishes a more comprehensive and in-depth comprehension of physical phenomena by revealing a greater number of travelling wave solutions. This exploration validates the effectiveness of the generalized ( ������������ & PRIME;)-Expansion method in resolving intricate fractional partial differential equations and underscores its potential for further investigation and application in a variety of fields. Lastly, this study demonstrates the effectiveness of the proposed approaches in discovering travelling wave solutions and shed light on the intricate behavior of waves through plotted graphs, thereby contributing to the body of knowledge on this subject.