On the Fractional Variable Order Thermostat Model: Existence Theory on Cones via Piece-Wise Constant Functions
Shahram Rezapour, Mohammed Said Souıd, Zoubida Bouazza, Azhar Hussain, Sina Etemad
Abstract
In the current manuscript, we intend to investigate the existence, uniqueness, and the stability of positive solution in relation to a fractional version of variable order thermostat model equipped with nonlocal boundary values in the Caputo sense. In fact, we will get help from the constant piece-wise functions for transforming our variable order model into an auxiliary standard model of thermostat. By Guo-Krasnoselskii’s fixed point theorem on cones, we derive the required conditions ensuring the existence property for positive solutions. An example is illustrated to examine the validity of the observed results.
Topics & Concepts
ThermostatUniquenessConstant (computer programming)MathematicsVariable (mathematics)Fixed-point theoremApplied mathematicsOrder (exchange)Property (philosophy)Mathematical analysisComputer sciencePhysicsEconomicsThermodynamicsEpistemologyProgramming languageFinancePhilosophyFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisNumerical methods in engineering