Optimal control problem of variable-order delay system of advertising procedure: Numerical treatment

Abstract

<p style='text-indent:20px;'>This paper presents an optimal control problem of the general variable-order fractional delay model of advertising procedure. The problem describes the flow of the clients from the unaware people group to the conscious or bought band. The new formulation generalizes the model that proposed by Muller. Two control variables are considered to increase the number of customers who purchased the products. An efficient nonstandard difference approach is used to study numerically the behavior of the solution of the mentioned problem. Properties of the proposed system were introduced analytically and numerically. The proposed difference schema maintains the properties of the analytic solutions as boundedness and the positivity. Numerical examples, for testing the applicability of the utilized method and to show the simplicity, accuracy and efficiency of this approximation approach, are presented with some comprising with standard difference methods.</p>