Abstract
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.
Highlights
Maybe it would have been a funny thing to talk about the possibility of mathematics helping the environment a few years ago
Mathematics can play a role if modeling comes to the point where we can do some of the chemical testing on computers. It is very important we increase our abilities in modern modeling by working on complicated fractional integro-differential equations and inclusions
We investigate the hybrid fractional differential inclusion model of the thermostat as
Summary
Maybe it would have been a funny thing to talk about the possibility of mathematics helping the environment a few years ago. They obtained existence results for the boundary value problem by applying the fixed point index theory on Hammerstein integral equations [7]. A set-valued operator G : [0, 1] → Pcl(R) is called measurable whenever the function t −→ dM(ω, G(t)) = inf{|ω – ν| : ν ∈ G(t)} is measurable for all real constant ω [15, 16].
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