@article{George2024, 
author = {Reny George and Sina Etemad and Fahad Sameer Alshammari},
title = {Stability analysis on the post-quantum structure of a boundary value problem: application on the new fractional    (  p  ,  q  )-thermostat system},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {1},
pages = {818-846},
keywords = {(p, q)-fractional calculus, (p, q)-gamma function, thermostat mathematical model, stability, fixed point},
url = {https://www.sciopen.com/article/10.3934/math.2024042},
doi = {10.3934/math.2024042},
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.}
}