Abstract
Langmuir waves propagate in fractal complex plasma with fractal characteristics, which may cause some plasma particles to be trapped or causes wave turbulences. This phenomenon appears in the form of fractional order equations. Using an effective unified solver, some new solitary profiles such as rational, trigonometrically and hyperbolical functions forms are discussed, using fractional derivatives in conformable sense. The fractional order modulates the solitary properties, such as amplitudes and widths. The proposition technique can be executed to study many applied science models.