Two compartmental fractional derivative model with fractional derivatives of different order

This study presents a new two compartmental model that contains fractional derivatives of different order. The model is so formulated that the mass balance is preserved. In this way we give an answer on a claim that such a model is not possible. The generalization that includes nonlinear terms and fractional order dynamics between compartments is also discussed. We derived a physically correct two compartmental system (i.e., the one preserving the mass balance) by the use of the Taylor expansion formula. Moreover, we derived in the Appendix such a system preserving the mass balance without the use of the Taylor formula but by the use of mass balance for systems with equal order fractional derivatives.

► Two compartmental model that contains fractional derivatives of different order is presented.
► The model is so formulated that the mass balance is preserved.
► The rates at which the drug enters or leaves compartment are not necessarily equal.
► The generalization includes nonlinear terms and fractional dynamics between compartments.
► System preserving the mass balance is derived both with and without Taylor formula.