New solitary wave solutions of generalized fractional Tzitzéica-type evolution equations using Sardar sub-equation method

In this study, Sardar sub-equation method is employed to obtain the solitary wave solutions for generalized fractional Tzitzéica type equations. By utilizing this method, novel solutions are derived for Tzitzéica, Tzitzéica Dodd–Bullough–Mikhailov and Tzitzéica–Dodd–Bullough equations in terms of fractional derivatives. The benefit of proposed method is that it offers a wide variety of soliton solutions, consisting of dark, bright, singular, periodic singular as well as combined dark-singular and combined dark–bright solitons. These solutions provide valuable insights into the intricate dynamics of generalized fractional Tzitzéica type evolution equations. The fractional wave and Painlevé transformation are utilized to transform the governing equation. The outcomes of our study are presented in a manner that highlights the practical utility and adeptness of fractional derivatives, along with the effectiveness of the proposed approach, in addressing a spectrum of nonlinear equations. Our findings reveal that the proposed method presents a comprehensive and efficient approach to explore exact solitary wave solutions for generalized fractional Tzitzeica type evolution equations.