A novel methodology for establishing a fractal-fractional oscillator and its application to the aggregation of grass carp's roes

This article examines the aggregation model of grass carp roe. This model is analogous to the Toda-like oscillator model, as any oscillation caused by perturbations will decay immediately. In general, the water environment on which fish depend for their survival does not need to be considered as a porous medium. However, in certain special water environments, the properties of the water may exhibit porous characteristics due to the presence of solid particles. In such instances, the consideration of porous medium characteristics of the water may assist in the more accurate description and comprehension of the aggregation mod-el of grass carp. The appropriate methodology is employed in this study in the traditional case. An alternative fractal system is proposed as a means of establishing the roe aggregation system in fractal space. This system is based on a Toda-like fractal-fractional system and has been demonstrated to exhibit analogous properties to integer order systems.