Modeling Fractional Dust-Acoustic Shock Waves in a Complex Plasma Using Novel Techniques

This work investigates how fractionality affects the dynamical behavior of dust-acoustic shock waves that arise and propagate in a depleted-electron complex plasma. This model consists of inertial negatively charged dust grains and inertialess nonextensive distributed ions. Initially, the fluid model equations that govern the propagation of nonlinear dust-acoustic shock waves are reduced to the integer Burgers-type equations using the reductive perturbation method. Thereafter, the integer Burgers-type equations are converted to the fractional cases using a suitable transformation. For analyzing this fractional family, both the Tantawy technique and the new iterative method are implemented within the Caputo sense framework. These methods can produce highly accurate analytical approximations without necessitating stringent assumptions or intricate computational processes, in contrast to other similar methods. Numerical examples and the calculation of the absolute error demonstrate the efficacy of the suggested methodologies, emphasizing their superior precision and swift convergence.