WAVES PROPAGATION AND SENSITIVITY VISUALIZATION FOR THE FRACTIONAL ORDER HEIMBURG MODEL IN BIOMEMBRANES AND NERVES

Abstract

In this paper, the fractional-order Heimburg model is under consideration analytically. This model has applications in the fields of pharmacology, neuroscience, cardiology, Biomembranes, and nerves. The newly modified extended direct algebraic method is used to gain the different types of exact solitary wave solutions. These solutions are successfully obtained in the form of dark, singular, complex singular, dark-singular, periodic, and rational functions. Additionally, getting the necessary aspects in accordance with the requirements is stimulated by the soliton's velocity. The wave profiles of the developed dynamical structural system are used to demonstrate the sensitivity and chaotic analysis, where the nerves wave singularity is controlled by the soliton wave velocity and wave number parameters. Lastly, the physical behavior of some extracted solutions is drawn by selecting the different values of parameters in the form of 3-dim and their corresponding contour plots. This work demonstrates that the technique used is efficient and can be applied to identify suitable closed-form solitary solitons to the dynamic study of Biomembranes and nerves.