Stability analysis on the post-quantum structure of a boundary value problem: application on the new fractional (p, q)-thermostat system

In this paper, we discussed some qualitative properties of solutions to a thermostat system in the framework of a novel mathematical model designed by the new (p, q)-derivatives in fractional post-quantum calculus. We transformed the existing standard model into a new control thermostat system with the help of the Caputo-like (p, q)-derivatives. By the properties of the (p, q)-gamma function and applying the fractional Riemann-Liouville-like (p, q)-integral, we obtained the equivalent (p, q)-integral equation corresponding to the given Caputo-like post-quantum boundary value problem ((p, q)-BOVP) of the thermostat system. To conduct an analysis on the existence of solutions to this (p, q)-system, some theorems were proved based on the fixed point methods and the stability analysis was done from the Ulam-Hyers point of view. In the applied examples, we used numerical data to simulate solutions of the Caputo-like (p, q)-BOVPs of the thermostat system with respect to different parameters. The effects of given parameters in the model will show the performance of the thermostat system.