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The fractional mapping equation method and fractional bi-function method are utilized to study a (2 + 1)-dimensional space-time fractional nonlinear Schrödinger equation, and its exact traveling wave solutions are constructed using the Mittag–Leffler function. These exact traveling wave solutions are used to analyze dynamical evolution of fractional solitons. The width and amplitude of these solitons remain unchanged. However, the shape of distorted M-shaped solitons and one of the distorted bright solitons remains unchanged, while waves are compressed and their widths reduce during increases in fractional parameters. Another distorted bright soliton has the opposite property, namely, the wave is broadened and its width enlarges during fractional parameter increases.