A Mathematical Model Approach Regarding the Children’s Height Development with Fractional Calculus
The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.
[1] Neyzi, O., Günöz, H., Furman, A., Bundak, R., Gökçay, G., & Darendeliler, F. (2008). Türk çocuklarında vücut ağırlığı, boy uzunluğu, baş çevresi ve vücut kitle indeksi referans değerleri. Çocuk Sağlığı ve Hastalıkları Dergisi, 51(1), 1-14.
[2] World Health Organization. WHO child growth standards: length/height for age, weight-for-age, weight-for-length, weight-for-height and body mass index-for-age, methods and development. World Health Organization, 2006.
[3] Kuczmarski, R. J. (2000). CDC growth charts; United States.
[4] Ogden, C. L., Kuczmarski, R. J., Flegal, K. M., Mei, Z., Guo, S., Wei, R., ... & Johnson, C. L. (2002). Centers for Disease Control and Prevention 2000 growth charts for the United States: improvements to the 1977 National Center for Health Statistics version. Pediatrics, 109(1), 45-60.
[5] Cole, T. J., & Green, P. J. (1992). Smoothing reference centile curves: the LMS method and penalized likelihood. Statistics in medicine, 11(10), 1305-1319.
[6] Cole, T. J. (1988). Fitting smoothed centile curves to reference data. Journal of the Royal Statistical Society: Series A (Statistics in Society), 151(3), 385-406.
[7] Waterlow, J. C., Buzina, R., Keller, W., Lane, J. M., Nichaman, M. Z., & Tanner, J. M. (1977). The presentation and use of height and weight data for comparing the nutritional status of groups of children under the age of 10 years. Bulletin of the world Health Organization, 55(4), 489.
[8] Demir, K., Özen, S., Konakçı, E., Aydın, M., & Darendeliler, F. (2017). A comprehensive online calculator for pediatric endocrinologists: CEDD Çözüm/TPEDS metrics. Journal of clinical research in pediatric endocrinology, 9(2), 182.
[9] Sabatier, J. A. T. M. J., Ohm Parkash Agrawal, and JA Tenreiro Machado. Advances in fractional calculus. Vol. 4. No. 9. Dordrecht: Springer, 2007.
[10] Axtell, Mark, and Michael E. Bise. "Fractional calculus application in control systems." Aerospace and Electronics Conference, 1990. NAECON 1990., Proceedings of the IEEE 1990 National. IEEE, 1990.
[11] Veliyev, Eldar I., et al. "The Use of the Fractional Derivatives Approach to Solve the Problem of Diffraction of a Cylindrical Wave on an Impedance Strip." Progress in Electromagnetics Research 77 (2018): 19-25.
[12] Škovránek, Tomáš, Igor Podlubny, and Ivo Petráš. "Modeling of the national economies in state-space: A fractional calculus approach." Economic Modelling 29.4 (2012): 1322-1327.
[13] Royston, Patrick, and Eileen M. Wright. "A method for estimating age‐specific reference intervals (‘normal ranges’) based on fractional polynomials and exponential transformation." Journal of the Royal Statistical Society: Series A (Statistics in Society) 161.1 (1998): 79-101.
[14] Royston, Patrick, and Douglas G. Altman. "Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling." Applied statistics (1994): 429-467.
[15] Gautschi, Walter. Numerical analysis. Springer Science & Business Media, 2011.
[1] Neyzi, O., Günöz, H., Furman, A., Bundak, R., Gökçay, G., & Darendeliler, F. (2008). Türk çocuklarında vücut ağırlığı, boy uzunluğu, baş çevresi ve vücut kitle indeksi referans değerleri. Çocuk Sağlığı ve Hastalıkları Dergisi, 51(1), 1-14.
[2] World Health Organization. WHO child growth standards: length/height for age, weight-for-age, weight-for-length, weight-for-height and body mass index-for-age, methods and development. World Health Organization, 2006.
[3] Kuczmarski, R. J. (2000). CDC growth charts; United States.
[4] Ogden, C. L., Kuczmarski, R. J., Flegal, K. M., Mei, Z., Guo, S., Wei, R., ... & Johnson, C. L. (2002). Centers for Disease Control and Prevention 2000 growth charts for the United States: improvements to the 1977 National Center for Health Statistics version. Pediatrics, 109(1), 45-60.
[5] Cole, T. J., & Green, P. J. (1992). Smoothing reference centile curves: the LMS method and penalized likelihood. Statistics in medicine, 11(10), 1305-1319.
[6] Cole, T. J. (1988). Fitting smoothed centile curves to reference data. Journal of the Royal Statistical Society: Series A (Statistics in Society), 151(3), 385-406.
[7] Waterlow, J. C., Buzina, R., Keller, W., Lane, J. M., Nichaman, M. Z., & Tanner, J. M. (1977). The presentation and use of height and weight data for comparing the nutritional status of groups of children under the age of 10 years. Bulletin of the world Health Organization, 55(4), 489.
[8] Demir, K., Özen, S., Konakçı, E., Aydın, M., & Darendeliler, F. (2017). A comprehensive online calculator for pediatric endocrinologists: CEDD Çözüm/TPEDS metrics. Journal of clinical research in pediatric endocrinology, 9(2), 182.
[9] Sabatier, J. A. T. M. J., Ohm Parkash Agrawal, and JA Tenreiro Machado. Advances in fractional calculus. Vol. 4. No. 9. Dordrecht: Springer, 2007.
[10] Axtell, Mark, and Michael E. Bise. "Fractional calculus application in control systems." Aerospace and Electronics Conference, 1990. NAECON 1990., Proceedings of the IEEE 1990 National. IEEE, 1990.
[11] Veliyev, Eldar I., et al. "The Use of the Fractional Derivatives Approach to Solve the Problem of Diffraction of a Cylindrical Wave on an Impedance Strip." Progress in Electromagnetics Research 77 (2018): 19-25.
[12] Škovránek, Tomáš, Igor Podlubny, and Ivo Petráš. "Modeling of the national economies in state-space: A fractional calculus approach." Economic Modelling 29.4 (2012): 1322-1327.
[13] Royston, Patrick, and Eileen M. Wright. "A method for estimating age‐specific reference intervals (‘normal ranges’) based on fractional polynomials and exponential transformation." Journal of the Royal Statistical Society: Series A (Statistics in Society) 161.1 (1998): 79-101.
[14] Royston, Patrick, and Douglas G. Altman. "Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling." Applied statistics (1994): 429-467.
[15] Gautschi, Walter. Numerical analysis. Springer Science & Business Media, 2011.
@article{"International Journal of Medical, Medicine and Health Sciences:78803", author = "Nisa Özge Önal and Kamil Karaçuha and Göksu Hazar Erdinç and Banu Bahar Karaçuha and Ertuğrul Karaçuha", title = "A Mathematical Model Approach Regarding the Children’s Height Development with Fractional Calculus ", abstract = "The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.
", keywords = "Children growth percentile, children physical development, fractional calculus, linear and polynomial model. ", volume = "13", number = "5", pages = "265-9", }
