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

Table 3

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

Results	Linear model
Age-body mass index		Polynomial model	Fractional model		Polynomial model	Fractional model		Polynomial model	Fractional model
	MAPE	MAPE	MAPE	Alfa	MAPE	MAPE	Alfa	MAPE	MAPE	Alfa
5%-boy	6.865466551	2.705373834	0.911126	0.001	2.63779053	0.651071	0.119	2.588440465	0.648818	0.129
15%-boy	6.915739985	2.704290105	1.319749	0.001	2.574127515	0.501764	0.101	2.425287783	0.499791	0.123
25%-boy	6.971573965	2.751387954	1.687045	0.001	2.515566244	0.558212	0.117	2.312195228	0.556502	0.137
50%-boy	7.016885183	2.810732896	2.213369	0.001	2.490436568	0.673523	0.142	2.14042388	0.652327	0.171
75%-boy	7.119935512	3.003870741	2.850619	0.001	2.570392019	0.87928	0.183	2.141484131	0.889948	0.217
85%-boy	7.114096202	3.018708576	3.018709	1	2.627532458	0.969604	0.205	2.060247302	0.973459	0.244
95%-boy	7.148701543	3.13331193	3.133312	1	2.804215436	1.121725	0.157	2.084685295	1.11742	0.278
5%-girl	6.855258661	3.231028281	1.659999	0.017	2.194516478	1.048393	0.261	2.264588115	0.925621	0.046
15%-girl	6.611929356	3.033530893	1.868429	0.001	2.086613692	0.946344	0.232	2.091314011	0.80253	0.065
25%-girl	6.465961229	2.968299158	2.088156	0.001	2.088687566	0.878275	0.218	2.043429311	0.794113	0.076
50%-girl	6.116695931	2.669341113	2.525415	0.001	2.106124203	0.865623	0.195	1.997292855	0.803468	0.069
75%-girl	5.740206516	2.516997789	2.516998	1	2.19501569	0.845701	0.1	1.957301328	0.85037	0.099
85%-girl	5.425758797	2.423741636	2.423742	1	2.253149389	0.767296	0.099	1.915490246	0.754622	0.139
95%-girl	5.270970139	2.383449508	2.38345	1	2.443491251	0.873101	0.043	2.064601668	0.677318	0.18
(M = 14)	6.545655683	2.811004601	2.185722		2.399118502	0.827136		2.149055829	0.7818790