Non-classical symmetry and analytic self-similar solutions for a non-homogenous time-fractional vector NLS system

Abstract The complex PDEs are a very important and interesting task in nonlinear quantum science. Although there have been extensive studies on the classical models, solving fractional models still has lot of shortcomings, especially for non-homogenous ones. Therefore, present study focuses two-component time-fractional NLS system, our method is to solve prolonged system derived from governed model. We first establish non-classical symmetries this new enlarged by using Lie group method. Then, with help Erdélyi–Kober operator, we reduce into ODEs, self-similar solutions obtained via power series expansion. convergence these proven as all variable coefficients analytic. Finally, generalize methods handle multi-component case. conclude that way may also bring some convenience other systems.