Abstract
The purpose of this paper is to apply a novel analytic algorithm based on Fractional Variational Iteration Method (FVIM) in order to examine the Multi-Dimensional Cable Equation with Variable Order Fractional with Non-Local Boundary Conditions Model (MDCEVOFNLBCM) with the Caputo variable time fractional derivative. In this method, initial and boundary conditions have been mixed together to get a new initial solution at every iteration. The convergence of method and the error estimation are given. The numerical analytical solution and some numerical examples show the accuracy and the efficiency of the proposed method, which is simple and accurate in comparison with exact. In addition, results are presented in Tables and Figure using both the MathCAD 12 and MATLAB software package.
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