"Numerical Studies of the Fractional Optimal Control Problem of Awarene" by Muner Mustafa Abou Hasan and Nasser Hassan Sweilam

Progress in Fractional Differentiation & Applications

Article Title

Numerical Studies of the Fractional Optimal Control Problem of Awareness and Trial Advertising Model

Authors

Muner Mustafa Abou Hasan, Department of Engineering Mathematics and Physics, Future University in Egypt, EgyptFollow
Nasser Hassan Sweilam, Department of Mathematics, Faculty of Science, Cairo University, Giza, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

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.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/080405

Recommended Citation

Mustafa Abou Hasan, Muner and Hassan Sweilam, Nasser (2022) "Numerical Studies of the Fractional Optimal Control Problem of Awareness and Trial Advertising Model," Progress in Fractional Differentiation & Applications: Vol. 8: Iss. 4, Article 5.
DOI: http://dx.doi.org/10.18576/pfda/080405
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol8/iss4/5

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