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.

中文翻译：

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具有混合边界值条件的恒温器的混合Caputo分数阶建模

我们将恒温器模型的二阶微分方程扩展为分数混合方程和包含形式。我们以混合条件的形式考虑该问题的边值条件。为了证明我们的混合分数恒温器方程和包含形式的解的存在性，我们将众所周知的Dhage不动点定理应用于单值和集值映射。最后，我们给出两个例子来说明我们的主要结果。