A Caputo discrete fractional-order thermostat model with one and two sensors fractional boundary conditions depending on positive parameters by using the Lipschitz-type inequality

Abstract A thermostat model described by a second-order fractional difference equation is proposed in this paper with one sensor and two sensors boundary conditions depending on positive parameters using the Lipschitz-type inequality. By means of well-known contraction mapping Brouwer fixed-point theorem, we provide new results existence uniqueness solutions. In work use Caputo operator Hyer–Ulam stability definitions check sufficient solution equations to be stable, while most researchers have examined necessary different ways. Further, also establish some regarding Hyers–Ulam, generalized Hyers–Ulam–Rassias, Hyers–Ulam–Rassias for our discrete fractional-order models. To support theoretical results, present suitable examples describing models that are illustrated graphical representation.