New soliton solutions for the space-time fractional modified third order Korteweg–de Vries equation

Abstract

In present research work, the soliton solutions of the space-time fractional modified third order Korteweg–de Vries (KdV) equation are explored by Sardar-subequation method (SSM). The (KdV) equation has an established version based on the shallow water waves in the oceans, oceanography theory and the ion-acoustic waves in plasma. The fractional order partial differential equation (PDE) is transform to a non-linear ordinary differential equation (ODE) by using traveling wave transformation. It is noted that in this work the fractional differential equation is solved in the sense of conformable derivative. Then soliton solutions of reduced equation are established by SSM. The present technique provides bright, dark, singular, periodic singular, combined bright-dark and combined dark-singular soliton solutions.