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

Table 1

results of age-body height to linear, Polynomial, and Fractional Model from 3 to 5 exponent numbers.

Results	Linear model
Age-height		Polynomial model	Fractional model		Polynomial model	Fractional model		Polynomial model	Fractional model
	MAPE	MAPE	MAPE	Alfa	MAPE	MAPE	Alfa	MAPE	MAPE	Alfa
3%-boy	5.402163228	2.947443454	0.879511614	0.506	1.450408	0.570475167	0.657	1.387619	0.43146	0.547
10%-boy	5.407534646	3.01494031	0.963707668	0.495	1.413681	0.534720874	0.661	1.337368	0.387715	0.56
25%-boy	5.464773802	3.060094876	1.034929851	0.483	1.40315	0.491194116	0.66	1.317915	0.363516	0.563
50%-boy	5.559953069	3.110350759	1.128587385	0.474	1.373834	0.440018959	0.665	1.272034	0.344825	0.587
75%-boy	5.632404553	3.163640075	1.22741669	0.462	1.391571	0.422563403	0.666	1.246001	0.354468	0.575
90%-boy	5.69813391	3.212386377	1.318764065	0.455	1.408876	0.435351278	0.671	1.224827	0.373018	0.617
97%-boy	5.776556168	3.272317243	1.40963534	0.447	1.422935	0.453567536	0.674	1.230354	0.393108	0.63
3%-girl	6.823285327	3.291558273	1.473083602	0.411	1.763813	0.605919002	0.62	1.344039	0.604952	0.622
10%-girl	6.9437678	3.218607376	1.431390254	0.416	1.736411	0.536266756	0.639	1.249269	0.549924	0.636
25%-girl	7.063383601	3.173419071	1.407654414	0.421	1.725992	0.475034474	0.64	1.149177	0.50914	0.7
50%-girl	7.193639107	3.0837981	1.357629583	0.427	1.719019	0.434119083	0.639	1.056893	0.463723	0.713
75%-girl	7.323473266	3.036228472	1.3501217	0.432	1.745766	0.446222807	0.637	0.983734	0.432988	0.715
90%-girl	7.450645847	2.991379294	1.337844927	0.438	1.749846	0.459484184	0.638	0.924253	0.429191	0.721
97%-girl	7.553575607	2.952629006	1.317973151	0.441	1.779546	0.486929947	0.636	0.882858	0.437864	0.742
(M = 14)	6.378092137	3.109199477	1.2598750174		1.577489142	0.485133399		1.18616721	0.4339922