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This work searches for new soliton solutions to the Atangana-Baleanu (AB) fractional system of equations for the ion sound and Langmuir waves (ISALWs). A new auxiliary equation scheme (NAES) is implemented to solve this model with the aid of a symbolic software. The hyperbolic and trigonometric function forms of this equation have been obtained. Due to the good performance of the NAEM, it is believed that this method is a promising technique to handle a wide variety of AB fractional evolution systems.