Affiliation:
1. Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
2. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
Abstract
<abstract><p>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.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
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