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

• Published in: Boundary value problems Vol. 2020; no. 1; pp. 1 - 16
• Main Authors: Baleanu, Dumitru, Etemad, Sina, Rezapour, Shahram
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 24.03.2020; Hindawi Limited; SpringerOpen
• 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; Hybrid fractional differential equation and inclusion; Thermostat modeling; Caputo fractional derivative; 34A12; 34A08
• ISSN: 1687-2770; 1687-2762; 1687-2770
• DOI: 10.1186/s13661-020-01361-0

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.