A Mathematical Approach with Fractional Calculus for the Modelling of Children’s Physical Development

Table 2

Results of age-body weight to linear, polynomial, and Fractional Model from 3 to 5 exponent numbers.

Results	Linear model
Age-body weight		Polynomial model	Fractional model		Polynomial model	Fractional model		Polynomial model	Fractional model
	MAPE	MAPE	MAPE	Alfa	MAPE	MAPE	Alfa	MAPE	MAPE	Alfa
3%-boy	15.94568859	8.124363119	2.225477998	0.51	3.984755	2.420906859	0.783	4.609962	2.36093	0.326
10%-boy	15.94129044	9.022159279	2.866036088	0.427	3.694552	2.313749619	0.787	3.961816	1.907708	0.376
25%-boy	16.10456514	9.835869013	3.633821445	0.342	3.483822	2.23629996	0.789	3.602703	1.476948	0.413
50%-boy	16.29961128	10.85175892	4.679024283	0.233	3.355553	2.12993533	0.785	3.358665	1.155057	0.465
75%-boy	16.29774355	11.7282567	5.574924231	0.134	3.317515	2.096470767	0.777	3.302717	1.209806	0.588
90%-boy	16.32249564	12.34877076	6.117002651	0.044	3.308995	1.944523119	0.76	3.19587	1.428124	0.043
97%-boy	16.0897	12.71400353	6.630194381	0.001	3.574042	1.792015967	0.733	3.092366	1.584805	0.001
3%-girl	13.26776061	12.7520431	6.308625438	0.161	3.945692	3.274024692	0.872	3.951722	2.24351	0.577
10%-girl	12.49925264	12.56753438	6.428139803	0.091	3.70836	2.868085155	0.841	3.695239	2.096702	0.694
25%-girl	11.66779732	12.25039184	6.319341635	0.001	3.548289	2.512683772	0.81	3.498459	2.094255	0.179
50%-girl	10.9204447	11.89221322	6.476098513	0.001	3.564722	2.080363121	0.762	3.36231	1.920233	0.001
75%-girl	10.08145527	11.55082465	7.025518322	0.001	3.919967	1.717374894	0.714	3.216609	2.127784	0.001
90%-girl	9.559115908	10.95681344	7.742623118	0.001	4.897397	1.589039883	0.641	3.061346	2.341874	0.866
97%-girl	9.216849965	10.54687482	8.867764628	0.001	5.917726	1.887806799	0.567	2.868494	2.171694	0.869
(M = 14)	13.586697932	11.22441976	5.778185181		3.87295621	2.204519995		3.48416271	1.8656735