Fractional Noether theorem and fractional Lagrange equation of multi-scale mechano-electrophysiological coupling model of neuron membrane

Abstract

Abstract Noether theorem is applied into a variable order fractional multiscale mechano-electrophysiological model of neuron membrane dynamics. The variable orders fractional Lagrange equation of a multiscale mechano-electrophysiological model of neuron membrane dynamics, is given. The variable orders fractional Noether symmetry criterion and Noether conserved quantities are given. The forms of variable orders fractional Noether conserved quantities correspond to Noether symmetry generators solutions of the model under different conditions are detailed discussed, and it is found that the expressions of variable orders fractional Noether conserved quantities are closely depending on the external nonconservative forces and material parameters of neuron.