Fractional traveling wave solutions of the (2 + 1)‐dimensional fractional complex Ginzburg–Landau equation via two methods

Abstract

A (2 + 1)‐dimensional fractional complex Ginzburg–Landau equation is solved via fractional Riccati method and fractional bifunction method, and exact traveling wave solutions including soliton solution and combined soliton solutions are constructed based on Mittag–Leffler function. A series of fractional orders is used to demonstrate the graphical representation and physical interpretation of the resulting solutions. The role of the fractional order is revealed.