Abstract
This article retrieves homoclinic breather solutions, M-shape rational solutions and their interactions for fractional quadratic-cubic nonlinear Schrodinger equation (FQC-NLSE) with the help of various appropriate transformation. We also formulate periodic cross kink waves, M-shaped with one and two kink, periodic cross rational, kink cross rational, interaction with M-shape, periodic and interaction with M-shape, rogue wave and I-kink for (FQC-NLSE). We will also plot 3-D, 2-D, contour and density graphs for newly computed solutions. The dynamics of above mentioned solutions are analysed graphically by choosing appropriate parametric values.