A hybrid Caputo fractional modeling for thermostat with hybrid boundary value conditions
Dumitru Bǎleanu, Sina Etemad, Shahram Rezapour
Abstract
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.
Topics & Concepts
ThermostatMathematicsOrdinary differential equationBoundary value problemExtension (predicate logic)Partial differential equationApplied mathematicsDifferential equationMathematical analysisFixed-point theoremSet (abstract data type)Fractional calculusComputer scienceThermodynamicsPhysicsProgramming languageFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisNumerical methods for differential equations