Progress in Fractional Differentiation & Applications

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In this article, a new nonstandard finite difference (NSFD) scheme was formulated to find an approximation numerical solution of the optimal control of the system of a generalized fractional model of the advertising problem. This system describes the flow of the customers from the unaware set to the aware or bought group. Properties of the studied system were introduced numerically and analytically. The utilized NSFD scheme keeps the attributes of the analytic solutions of the proposed system as positivity and boundedness. To test the behavior of the proposed method, numerical examples are run out with some comprising with standard finite difference method and forward-backward sweep method. The results show the simplicity, accuracy, and applicability of this approximation method.

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