Exploration of bifurcation, chaos and novel optical dromions solution of the fractional nonlinear dynamical model

This work explores the time-space fractional soliton neuron model (TSFSNM), a framework that accounts for the inherent time-space nonlinearity prevalent across various fields, including mathematical physics, nonlinear dynamics, and engineering disciplines such as neurosciences, biosciences, fluid mechanics, plasma physics, and geochemistry. The innovation of this paper lies in introducing and employing advanced fractional modeling techniques, namely the modified Sardar sub-equation (MSSE) method and the improved F-expansion method. We construct explicit analytical solutions, offering insights into the solitary sound pulses that represent signals passing through the cell membrane (CM). These pulses are modeled as solitons, capturing the localized dynamics of neuronal communication. Furthermore, bifurcation and sensitivity analysis provide a deeper understanding of the influence of fractional-order parameters on the system's behavior. The findings emphasize the significance of fractional soliton models in describing complex wave phenomena in diverse scientific and engineering contexts.