English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this study, after we have briefly introduced the standard Gross-Pitaevskiiequation, we have suggested fractional Gross-Pitaevskii equations toinvestigate the time-dependent ground state dynamics of the Bose-Einsteincondensation of weakly interacting bosonic particle system which can includesnon-Markovian processes or non-Gaussian distributions and long-rangeinteractions. Only we focused the time-fractional Gross-Pitaevskii equation andhave obtained solutions of the standard Gross-Pitaevskii and time-fractionalGross-Pitaevskii equations for attractive and repulsive interactions in thecase external trap potentials $V(x)=0$ and optical lattice potential $V(x)=\pm\sin^{2}x$ by using Homotopy Perturbation Method. We have found that theHomotopy Perturbation Method solutions of the Gross-Pitaevskii equation forthese potentials and interactions are the same analytical results of it.Furthermore we have also found that solutions of the time-fractionalGross-Pitaevskii equation for these potentials and interactions can be given interms of Mittag-Leffler function. The solutions of the time-fractionalGross-Pitaevskii equation provide that the time evolution of the ground statedynamics of Bose-Einstein condensation of bosonic particles deviatesexponential form, and evolutes with time as stretched exponentially.

Solutions of the Gross-Pitaevskii and time-fractional Gross-Pitaevskii equations for different potentials with Homotopy Perturbation Method