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. 2023 Jun 21;13:10083. doi: 10.1038/s41598-023-37196-9

Table 1.

The obtained models.

Treated case Untreated case
Integer order exponential model dvdt=0.046·vt dvdt=0.109·vt
Fractional order exponential model dv0.97dt=0.046·vt dv0.98dt=0.109·vt
Integer order logistic model dvdt=0.0735·vt·1-vt2.813.35 dvtdt=0.565·vt·1-vt35.20.134
Fractional order logistic model dv0.94tdt=0.0735·vt·1-vt2.813.35 dv0.88tdt=0.565·vt·1-vt35.20.134
Integer order Gompertz model dvtdt=0.204ln8.81vt+5.04 dvtdt=0.106ln26.09vt+2.24
Fractional order Gompertz model dv0.95tdt=0.204ln8.81vt+5.04 dv0.86tdt=0.106ln26.09vt+2.24
Integer order generalized Bertalanffy–Pütter model dvdt=0.168·v2.18-0.1·v2.66 dvdt=0.894·v1.38-0.741·v1.44
Fractional order generalized Bertalanffy–Pütter model dv0.96dt=0.168·v2.18-0.1·v2.66 dv0.96dt=0.894·v1.38-0.741·v1.44
Integer order particularized Bertalanffy–Pütter model dvdt=0.064v2.41-lnv·0.063·v2.41 dvdt=0.203v0.74-lnv·0.011·v0.74
Fractional order particularized Bertalanffy–Pütter models model dv0.96dt=0.064v2.41-lnv·0.063·v2.41 dv0.95dt=0.203v0.74-lnv·0.011·v0.74