We attempt to motivate utilization of some local derivatives of arbitrary orders in clinical medicine. For this purpose, we provide two efficient solution methods for various problems that occur in nature by employing the local proportional derivative defined by the proportional derivative (PD) controller. Under some necessary assumptions, a detailed exposition of the instantaneous volume in a lung is furnished by conformable derivative and such modified conformable derivatives as truncated M-derivative and proportional derivative. Moreover, we wish to investigate the performance of the above-mentioned operators in applications by plotting several graphs of the governing equations.

我们试图激发临床医学中任意顺序的一些局部导数的利用。为此，我们采用比例微分（PD）控制器定义的局部比例微分，为自然界中发生的各种问题提供了两种有效的解决方法。在一些必要的假设下，通过适形导数以及诸如截短的M-导数和比例导数之类的修饰的适形导数提供了肺中瞬时体积的详细说明。此外，我们希望通过绘制几个控制方程图来研究上述算子在应用中的性能。