We provide an extension for the second-order differential equation of a thermostat model to the fractional hybrid equation and inclusion versions. We consider boundary value conditions of this problem in the form of the hybrid conditions. To prove the existence of solutions for our hybrid fractional thermostat equation and inclusion versions, we apply the well-known Dhage fixed point theorems for single-valued and set-valued maps. Finally, we give two examples to illustrate our main results.
MSC: Primary 34A08; secondary 34A12Keywords: Caputo fractional derivative; Hybrid fractional differential equation and inclusion; Thermostat modelingh(t,z(t)) ] + g(t, z(t)) = 0 (t ∈ [0, 1], p ∈ (1, 2]), z(0) = z(1) = 0.