New fractional solutions for the Clannish Random Walker’s Parabolic equation and the Ablowitz-Kaup-Newell-Segur equation

In this article, we find fractional solutions for the Clannish Random Walkers Parabolic (CRWP) equation and Ablowitz-Kaup-Newell-Segeur (AKNS) equation. Different areas of applied sciences, the study of these equations plays a significant role. We select two methods for this purpose, firstly new recent well-established technique is improved Auxiliary equation scheme and second technique is \((\frac{G^{'}}{G^{2}})\) $(\frac{G^{{}^{\prime }}}{G^2})$ -technique with the help of beta derivative. We used fractional term which involves in beta derivative, in our selected mathematical models. To show how the obtained solutions physically look, they plotted different profiles including both 2D and 3D graphics.