This study is intended to provide an exhaustive comparison of various non-local fractional operators when analyzing the mechanics of breathing performed by a ventilator. We present the solutions of the fractional respiratory mechanics model mainly for allowing the health care team to monitor patients' conditions in detail. The aim is to introduce the underlying model flexibly by making use of the advantages of the non-integer order operators with one, two, and three parameters. On the other

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... , since we concern the usage of different types of fractional operators, most often having virtue in the application, it can be clearly observed the similarities and differences between these operators. Moreover, we observe the mobility of the solutions curves of the above-stated fractional model for different values of the parameters $\alpha$, $\rho$, and $\gamma$ with the help of many graphs.