Abstract
In this article, the fractional third-order dispersive partial differential equations were investigated by using Shehu decomposition and variational iteration transform methods. The well known Riemann-Liouville fraction integral, Caputo's fractional-order derivative, Shehu transform for fractional-order derivatives and Mittag-Leffler function were used as the major basis of the methodology. The graphs and table show the solution behavior for various fractional order values. The comparison provided the signed agreement of the solutions to each other as well as with the exact result. The accurateness and efficiency of the suggested techniques are examined using two numerical experiments. The reliability and validity tests show that for various fractional-order values, the newly proposed method is reliable, accurate, and efficient.