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Fractional Order Financial Models for Awareness and Trial Advertising Decisions

Author

Listed:
  • Benito Chen-Charpentier

    (University of Texas at Arlington)

  • Gilberto González-Parra

    (University of Texas at Arlington
    Universidad de los Andes)

  • Abraham J. Arenas

    (Universidad de Córdoba)

Abstract

Advertising is a type of communication that can be used to encourage, persuade, or manipulate an audience to continue or take some new action. The most common application is to drive consumer behavior with respect to products or services. However, political and ideological advertising has been increasing in the last decades. Different models has been proposed to investigate dynamic advertising problems in business and economics fields. Since the effect of advertising is not instantaneous we present a fractional order model to explain and understand advertising with two components: awareness and trial advertising. In the fractional model the next state depends not only upon its current state but also upon all of its previous states. In order to deal with the fractional derivatives of the model we rely on the Caputo operator and use a predictor-corrector method to numerically approximate the fractional derivatives.

Suggested Citation

  • Benito Chen-Charpentier & Gilberto González-Parra & Abraham J. Arenas, 2016. "Fractional Order Financial Models for Awareness and Trial Advertising Decisions," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 555-568, December.
    • Handle: RePEc:kap:compec:v:48:y:2016:i:4:d:10.1007_s10614-015-9546-z
    DOI: 10.1007/s10614-015-9546-z
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    References listed on IDEAS

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    1. Menghan Wang & Qinglong Gou & Chunxu Wu & Liang Liang, 2013. "An aggregate advertising response model based on consumer population dynamics," International Journal of Applied Management Science, Inderscience Enterprises Ltd, vol. 5(1), pages 22-38.
    2. W.H. Ip & K.L. Yung & Dingwei Wang, 2012. "A chaotic model for advertising diffusion problem with competition," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(8), pages 1545-1554.
    3. Huang, Jian & Leng, Mingming & Liang, Liping, 2012. "Recent developments in dynamic advertising research," European Journal of Operational Research, Elsevier, vol. 220(3), pages 591-609.
    4. Škovránek, Tomáš & Podlubny, Igor & Petráš, Ivo, 2012. "Modeling of the national economies in state-space: A fractional calculus approach," Economic Modelling, Elsevier, vol. 29(4), pages 1322-1327.
    5. Yanqin Liu, 2012. "Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    6. Adel Al-Rabtah & Shaher Momani & Mohamed A. Ramadan, 2012. "Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. Kamrad, Bardia & Lele, Shreevardhan S. & Siddique, Akhtar & Thomas, Robert J., 2005. "Innovation diffusion uncertainty, advertising and pricing policies," European Journal of Operational Research, Elsevier, vol. 164(3), pages 829-850, August.
    8. Muller, Eitan, 1983. "Trial/awareness advertising decisions : A control problem with phase diagrams with non-stationary boundaries," Journal of Economic Dynamics and Control, Elsevier, vol. 6(1), pages 333-350, September.
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    1. Ogochukwu Ifeacho & Gilberto González-Parra, 2025. "Mathematical Modeling of Economic Growth, Corruption, Employment and Inflation," Mathematics, MDPI, vol. 13(7), pages 1-32, March.

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