Abstract

In this paper, we investigate the fractional-order arms race model. The model has emerged as an important tool for the investigation of international conflict and arms races. The variational iteration method, the homotopy perturbation method, and the adomian decomposition method are used to solve the mathematical model with Caputo's fractional derivative. Several numerical computations have been provided to establish the validity and accuracy of the acquired results. It is shown that the fractional-order model can be solved easily using semi-analytical methods. The results obtained by all methods are compared.

Keywords and Phrases

Richard's Arms Race Model, Reimann-Liouville Fractional Integral, Caputo Fractional Derivative, Variational Iteration Method, Adomian Decomposition Method, Homotopy Perturbation Method.

A.M.S. subject classification

26A33, 35A99, 91B74.

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