On The Propagation of Soliton Solution in Comb-like Model

In present work, comb-like model (toy model has proven valuable to ‎explain and quantify the transport along spin dendrites like for instance ‎nerve cell conduction) as a fractal background medium has been used to ‎derive the well-known nonlinear fractional KdV equation where time ‎evolution operator admits half-order (α=1/2). We investigate the effect of ‎the presence of infinite fingers of our suggest model to the propagation of ‎soliton solution along back bone of structure by employing the travelling ‎wave transform method in order to obtain the corresponding soliton ‎solution. The time fractional operator causes a remarkable change on the ‎soliton profile in both width and amplitude. The main results of this study ‎show the sensitive dependence of soliton profile (width and amplitude) ‎on the fractional exponent of time evolution operator. This means that ‎fractal geometry like spines dendrites structure enhanced the propagation ‎of soliton profile along the backbone of the structure due to the increasing ‎of the amplitude and decreasing its width. In addition to there are no ‎effect on the form of soliton with variation of time fractional operator. ‎Finally, we can say that, Comb-like model provide a good geometrical ‎explanation of anomalous transport. ‎