A unifying computational framework for fractional Gross–Pitaevskii equations

Abstract

This paper concerns investigating the complex behaviour of the special case of Schrödinger equation called Gross–Pitaevskii (GP) equations using -homotopy analysis transform method (-HATM) with fractional order. Based on denticity function and different initial conditions, we consider three different examples to demonstrate the proficiency of -HATM. We consider different initial conditions for the hired system and the projected method is elegant unification of -homotopy analysis algorithm and Laplace transform. Further, the physical natures of the achieved results have been captured for change in space, time, homotopy parameter and fractional order in terms of contour and surface plots, and the accuracy is presented with the numerical study. The obtained results conclude that, the hired technique is highly methodical, easy to implement and accurate to examine the behaviour of the nonlinear equations of both fractional and integer order describing allied areas of science.