In this paper, we investigate the conformable derivative effect on the travelling wave solutions for extended \((3+1)\) -dimensional Kudryashov’s equation with generalized anti-cubic nonlinearity. To accomplish this, we employ the improved modified extended tanh-function method, which enables us to obtain diverse optical soliton solutions. A variety of distinct traveling wave solutions are furnished. The obtained solutions comprise dark solitons, bright solitons, singular solitons and singular periodic. The impact of the fractional derivative is illustrated graphically using examples of some of the retrieved solutions with various values of fractional order. It is worth noting that the proposed method, being effective, consistent, and influential, can be applied to solve various other physical models and related disciplines.
