Enhanced analysis of soliton-like pulses in space-time fractional beta-derivatives coupled nerve fibers with application insights  

Abstract

This work aims to delve exact physical wave solutions of nonlinear differential-difference equations with beta-derivative leading the conduction of nerve impulse dynamics in coupled nerve fibers. The technique performed here names the polynomial expansion method. By employing a new variable through a fractional complex transformation, we turn the electrical model equation to a second-order elliptic nonlinear ordinary differential equation with two free parameters including the semi-discrete approximation. We extract short pulse, kink, anti-kink, singular kink/anti-kink and kink-rogue solitary waves as solutions of the derived elliptic nonlinear ordinary differential equations. By carrying out these various solutions, we peruse the dynamical behavior of the current nerve fibers model by investigating their linear stability. We also study the dynamics of the model by applying the fixed points theory and derive the related Jacobian matrix. Throughout the convenient physiological parameters values and signs, we display some 3D modulational instability zones. Furthermore, we also exhibit 3D and 2D graphs presenting the shapes of new pursued solitary waves. The numerous solutions families obtained and plotted help us to show the fractional-order parameter effects in addition of the nerve fiber diameter on the amplitude and speed of the nerve impulse propagating inside the coupled nerve fibers. The good or bad coordination of the movement inside the human parts can be explain through the amplitude varying, speed modification of the nerve impulse flowing into the coupled nerve fibers. Aiming to this, we make the evolved mathematical framework accessible and highlight potential medical and biological applications. In addition, we enhance the understanding of nerve conduction mechanisms in myelinated fibers.