This study presents two new numerical techniques for solving time-fractional one-dimensional cable differential equation (FCE) modeling neuronal dynamics. We have introduced new formulations for the approximate-analytical solution of the FCE by using modified homotopy perturbation method defined with conformable operator (MHPMC) and reduced differential transform method defined with conformable operator (RDTMC), which are derived the solutions for linear-nonlinear fractional PDEs. In order to show the efficiencies of these methods, we have compared the numerical and exact solutions of fractional neuronal dynamics problem. Moreover, we have declared that the proposed models are very accurate and illustrative techniques in determining to approximate-analytical solutions for the PDEs of fractional order in conformable sense.
Yavuz, Mehmet and Yaşkıran, Burcu
Conformable Derivative Operator in Modelling Neuronal Dynamics,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 13,
2, Article 13.
Available at: https://digitalcommons.pvamu.edu/aam/vol13/iss2/13