A hybrid Caputo fractional modeling for thermostat with hybrid boundary value conditions

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...

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Bibliographic Details
Published in:Boundary value problems 2020-03, Vol.2020 (1), p.1-16, Article 64
Main Authors: Baleanu, Dumitru, Etemad, Sina, Rezapour, Shahram
Format: Article
Language:English
Subjects:
Analysis
Approximations and Expansions
Boundary value problems
Caputo fractional derivative
Difference and Functional Equations
Differential equations
Fixed points (mathematics)
Hybrid fractional differential equation and inclusion
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Thermostat modeling
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Summary: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.
ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-020-01361-0