In this study, let’s find the soliton solutions of the perturbed nonlinear Chen–Lee–Liu equation via the new fractional derivative operator in following form iℵα hyp,tƛ(x, t) + aℵ2α hyp,xƛ(x, t) + ib|ƛ(x, t)|ℵα hyp,xƛ = i[λℵα hyp,xƛ(x, t)+ θℵα hyp,x|ƛ(x, t)|2mƛ(x, t) + σƛ(x, t)ℵα hyp,x ( |ƛ(x, t)|2m ) , by using the extended hyperbolic method. This equation is one of the most widely used models in mathematics and physics, which requires the study of this equation with different and practical methods. One of these methods is the extended hyperbolic approach, which is discussed and analyzed in this article. Since this equation has a very wide application in particle physics, how to study it is very important. Therefore, it is very important to use methods that include a wide range of answers. This method can also be very useful because it has a variety of answers, which we can see in the obtained answers. The solutions obtained in this article are new and more accurate than the studies done so far
