Generalized analysis of fractional Dullin-Gottwald-Holm equation: Soliton solutions and their applications in non-linear wave dynamics - Yousef Jawarneh; Ali H. Hakami; Abaker A. Hassaballa (Ain Shams Engineering Journal)
This research work explores fractional Dullin-Gottwald-Holm equation with Katugampola fractional derivatives via novel application of the generalized Riccati-Bernoulli sub-ODE approach in conjunction with the Bäcklund transformation. We develop fresh plethora of perturbed kink structures, kink and anti-kink soliton solutions using well-established criteria, and we evaluate their intricate behavior patterns. This study examines the impact of variations in the fractional-order parameter α on the soliton solutions through 2D graphical representations that reveal key insights into fractional-order effects. To illustrate the solitons' complex structure and formation, we combine contour plots with 3D graphs. This study advances our understanding of wave nonlinearity in complexly dynamic physical systems. Our work illustrates the influence of fractional parameters on solution behaviors, with broad implications for fluid mechanics and non-linear wave theory. This method's efficacy and adaptability show that it has the potential to tackle challenging non-linear problems and uncover a variety of fascinating physical phenomena.