Dynamics of fractional order modified Morris-Lecar neural model

Most of the beautiful biological functions in neural systems are expected to happen considering the system with memory effect. Fractional differential equations are very useful to investigate long-range interacting systems or systems with memory effect. In this paper, a fractional order nonlinear three dimensional modified Morris-Lecar neural system (M-L system) has been studied. The fractional order M-L system is a generalization of the integer order M-L system. The paper presents an approximate analytical solution of the fractional order M-L system, using Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM). The fractional derivatives are described in the Caputo sense. We have used the above methods as they show very efficient result for very small time region. Solutions are obtained in the form of rapidly convergent infinite series and only a few iterations are needed to obtain the approximate solutions. Comparison of both HPM and VIM reveals that the two present methods of solution are elegant and powerful for solving the nonlinear fractional order biological as well as neural systems.