<p>A nonlinear fractional differential equation with variable order Caputo fractional derivative with respect to another function is studied. We consider the case of a piecewise constant variable order of the fractional derivative and we apply three types of fractional derivatives to differential equations. Also we define a solution of the initial value problem for differential equations with the corresponding fractional derivative. In addition, we use the three types of variable order Caputo fractional derivatives with respect to another functions to a chemical engineering model about the concentration of the chemical reaction. The application of these types of derivatives potentially allow us to more adequately model the dynamics of the concentrations. The chemical engineering model in this paper is simulations of a chemical engineering model in the literature and we hope in the future our model will have applications in real life phenomena. We establish the finite time stability of the models and in addition, we illustrate on particular examples the influence of the applied derivatives on the behavior of the model. As special cases, we obtain the finite time stability results for models with the Caputo derivative with constant order.</p>