  Abstract The present work describes a new fractional-order system of a
two-compartment CA3 hippocampal pyramidal cell, which is known as Pinsky-Rinzel
model with Caputo fractional derivative. Firstly, The transient of the
solutions is investigated. Then based on the bifurcation diagrams, we study the
general behavior of the system. In this case, fractional derivative order and
currents injection, are taken as bifurcation parameters. Chaotic regions are
obtained for different values of the fractional derivative order and different
injection currents. Finally, a numerical approach is introduced to study the
stability of the system under certain conditions. The obtained results can be
considered as help to control relevant diseases caused by maximal injection
currents abnormality.
