This paper is about the study of space-time fractional Fokas-Lenells
equation that describes nonlinear wave propagation in optical fibers.
Three prominent schemes are employed for extracting different types of
exact soliton solutions. In particular, the expa function method, the
hyperbolic function method and the simplest Riccati equation scheme are
investigated for the said model. As a sequela, a series of soliton
solutions are obtained and verified through Mathematica. The obtained
solutions are significant additions in some specific fields of physics
and engineering. Furthermore, the 3D graphical descriptions are left to
analyze the pulse propagation for the reader.