3,311 research outputs found
Conformable Derivative Operator in Modelling Neuronal Dynamics
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
Reduced Differential Transform Method for (2+1) Dimensional type of the Zakharov-Kuznetsov ZK(n,n) Equations
In this paper, reduced differential transform method (RDTM) is employed to
approximate the solutions of (2+1) dimensional type of the Zakharov-Kuznetsov
partial differential equations. We apply these method to two examples. Thus, we
have obtained numerical solution partial differential equations of
Zakharov-Kuznetsov. These examples are prepared to show the efficiency and
simplicity of the method
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