Vector optical soliton and periodic solutions of a coupled fractional nonlinear Schrödinger equation

•Solutions of space-time fractional CNLSE are derived.•Fractional Riccati method and Fractional dual function method are presented.•Two- and three-dimensional graphs of vector optical solitons are displayed. A coupled space-time fractional nonlinear Schrödinger equation is solved by the fractional Riccati method and fractional dual-function method. By choosing the appropriate values of parameters, we obtain exact analytical vector soliton and periodic solutions constructed by the Mittag–Leffler function and give the special conditions for the formation of solitons. The two- and three-dimensional graphs of these solutions are displayed. These solutions are helpful to understand the complex physical and engineering problems described by the coupled space-time fractional nonlinear Schrödinger equation.