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

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.

Noether’s Theorem of Herglotz Type for Fractional Lagrange System with Nonholonomic Constraints

“…According to the Appell-Chetaev condition (14) and the commutative relation (15), we can easily obtain…”

“…Atanacković et al [9] derived the fractional Noether theorem under the classical definition of conserved quantity, which reveals the inherent connection between Noether symmetry transformations and fractional-order conserved quantities. In recent years, the study of conserved quantities and symmetries in fractional mechanics using variational methods has made some headway [10][11][12][13][14][15][16][17][18].…”

Symmetries and perturbations of time-scale nonshifted singular systems

“…1 As is well known, there are three standard classical symmetries. The Noether symmetry [2][3][4][5] is the invariance of an action functional under the infinitesimal transformation of a group and can be used to derive a Noether conserved quantity. The Lie symmetry 6,7 is the invariance of differential equations under the tiny change of a group and can be used to derive Hojman conserved quantities.…”