Akhtar Hussain, Tarek F. Ibrahim, Fathea M. Osman Birkea, Maan A. Yahya, Abaker A. Hassaballa, Herbert Mukalazi
This research focuses on investigating soliton solutions for the space-time fractional modified third-order Korteweg-de Vries equation using the auxiliary equation method. The Korteweg-de Vries equation is renowned for its application in modeling shallow-water waves, oceanographic dynamics, and ion-acoustic waves in plasma. By employing a traveling wave transformation, the fractional-order partial differential equation is converted into a nonlinear ordinary differential equation. This study used conformable derivatives to solve the fractional differential equation. Soliton solutions, including bright, dark, singular, periodic singular, combined bright-dark, and combined dark-singular forms, are derived through the application of auxiliary equation method to the reduced equation.