Myelinated neurons are characterized by the presence of myelin, a
multilaminated wrapping around the axons formed by specialized neuroglial
cells. Myelin acts as an electrical insulator and therefore, in myelinated
neurons, the action potentials do not propagate within the axons but happen
only at the nodes of Ranvier which are gaps in the axonal myelination. Recent
advancements in brain science have shown that the shapes, timings, and
propagation speeds of these so-called saltatory action potentials are
controlled by various biochemical interactions among neurons, glial cells, and
the extracellular space. Given the complexity of brain's structure and
processes, the work hypothesis made in this paper is that non-local effects are
involved in the optimal propagation of action potentials. A space-fractional
cable equation for the action potentials propagation in myelinated neurons is
proposed that involves spatial derivatives of fractional order. The effects of
non-locality on the distribution of the membrane potential are investigated
using numerical simulations.Comment: 20 pages, 14 figures; added reference, updated formulas, added new
formulas, corrected typos, added 4 figure
