Solution of generalised fuzzy fractional Kaup–Kupershmidt equation using a robust multi parametric approach and a novel transform

Abstract

This work considers a fuzzy fractional model of the Kaup–Kupershmidt equation with uncertain initial conditions. The uncertain behaviour of capillary gravity and dispersive waves is studied using a robust double parametric fuzzy approach termed the q-Homotopy analysis method with a generalised novel transform. The proposed method’s accuracy and efficiency have been explained by comparing the observation of fuzziness in the solution with several prior accessible results for the crisp case using the double parametric approach. This methodology provides a viable alternative to existing methods for various fuzzy fractional models.