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Bioinformatics of the Brain

• Exponential model is represented with differential equation

dV (t)

dt

= aV (t), max.size ∞and growth condition is a > 0,

• Logistic model is represented with differential equation

dV (t)

dt

= aV (t)(1 −^{V (t)}

V∞

), max.size V∞= a/b and growth condition is a > 0,

• Gompertz model is represented with differential equation

dV (t)

dt

= bV (t)ln( ^V∞

V (t)^{) , max.size V∞= ln−1(a/b) and growth condition is}

b > 0,

• Bertalanffy model is represented with differential equation

dV (t)

dt

= aV (t)^2/3 −bV (t), max.size is V∞= (a/b)³ and growth condition is

a > b,

• Guiot −West model is represented with differential equation

dV (t)

dt

= aV (t)^3/4 −bV (t), max.size is V∞= (a/b)⁴ and growth condition is

a > b.

The study’s findings indicate that each model’s fractional version outperforms

its integer order equivalents in terms of indicators. Numerical findings imply

that fractional models can be important to tumor prediction.

It may be worthwhile to investigate the details and characteristics of frac-

tional calculus in connection to the measurement of tumor development. A

potential explanation for the better prediction accuracy of fractional models

might be the memory effect, which is a natural consequence of the non-integer

order derivative specification. Considering that cells in tumors have accumu-

lated several mutations and alterations throughout their development, frac-

tional models may be able to account for these non-local (past) occurrences.

Another intriguing pattern is that larger, rapidly growing tumors appear to be

best demonstrated using fractional orders. The previously stated models have

to be taken into consideration in order to support therapeutic advice. Even

though the initial findings and potential characteristics are very promising,

further research has to be done, especially to find out how versatile arbitrary

order α is and to compare these models to other experimental sets of data

and advice [34].