Akram, GhazalaSadaf, MaasoomahZainab, IqraAbbas, MuhammadAkgul, Ali2024-12-242024-12-2420232504-3110https://doi.org/10.3390/fractalfract7090665https://hdl.handle.net/20.500.12604/8216The time-fractional nonlinear Drinfeld-Sokolov-Wilson system, which has significance in the study of traveling waves, shallow water waves, water dispersion, and fluid mechanics, is examined in the presented work. Analytic exact solutions of the system are produced using the modified auxiliary equation method. The fractional implications on the model are examined under b-fractional derivative and a new fractional local derivative. Extracted solutions include rational, trigonometric, and hyperbolic functions with dark, periodic, and kink solitons. Additionally, by specifying values for fractional parameters, graphs are utilized to comprehend the fractional effects on the obtained solutions.eninfo:eu-repo/semantics/openAccesstime fractional nonlinear Drinfeld-Sokolov-Wilson systembeta-fractional derivativea new local fractional derivativemodified auxiliary equation methodArticle79Q1WOS:001073863400001Q12-s2.0-8517218064510.3390/fractalfract7090665