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

Abstract

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.

Keywords

• (p， q) -fractional calculus
• (p， q) -gamma function
• thermostat mathematical model
• stability
• fixed point