OPTIMAL CONTROL PROBLEM OF VARIABLE-ORDER DELAY SYSTEM OF ADVERTISING PROCEDURE: NUMERICAL TREATMENT

NASSER H. SWEILAM; TAGHREED A. ASSIRI; MUNER M. ABOU HASAN

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OPTIMAL CONTROL PROBLEM OF VARIABLE-ORDER DELAY SYSTEM OF ADVERTISING PROCEDURE: NUMERICAL TREATMENT

机译：OPTIMAL CONTROL PROBLEM OF VARIABLE-ORDER DELAY SYSTEM OF ADVERTISING PROCEDURE: NUMERICAL TREATMENT

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This paper presents an optimal control problem of the generalvariable-order fractional delay model of advertising procedure. The problemdescribes the flow of the clients from the unaware people group to the consciousor bought band. The new formulation generalizes the model that proposedby Muller. Two control variables are considered to increase the numberof customers who purchased the products. An efficient nonstandard differenceapproach is used to study numerically the behavior of the solution ofthe mentioned problem. Properties of the proposed system were introducedanalytically and numerically. The proposed difference schema maintains theproperties of the analytic solutions as boundedness and the positivity. Numericalexamples, for testing the applicability of the utilized method and toshow the simplicity, accuracy and efficiency of this approximation approach,are presented with some comprising with standard difference methods.

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《Discrete and continuous dynamical systems, Series S》 |2022年第5期|1247-1268|共22页
作者
NASSER H. SWEILAM; TAGHREED A. ASSIRI; MUNER M. ABOU HASAN;
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作者单位

Department of Mathematics, Faculty of ScienceCairo University, Giza, Egypt;

Department of Mathematics, Faculty of ScienceUmm Al-Qura University, Saudi Arabia;

Department of Engineering Mathematics and PhysicsFuture University in Egypt, Egypt;

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Financial models of awareness and trial; variable-order fractional delay optimal control problem; Caputo variable-order fractional derivative; nonstandard finite difference technique;

OPTIMAL CONTROL PROBLEM OF VARIABLE-ORDER DELAY SYSTEM OF ADVERTISING PROCEDURE: NUMERICAL TREATMENT

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