On the qualitative analysis of the fractional boundary value problem describing thermostat control model via ψ-Hilfer fractional operator
Chatthai Thaiprayoon, Weerawat Sudsutad, Jehad Alzabut, Sina Etemad, Shahram Rezapour
Abstract
Abstract In this research study, we are concerned with the existence and stability of solutions of a boundary value problem (BVP) of the fractional thermostat control model with ψ -Hilfer fractional operator. We verify the uniqueness criterion via the Banach fixed-point principle and establish the existence by using the Schaefer and Krasnoselskii fixed-point results. Moreover, we apply the arguments related to the nonlinear functional analysis to discuss various types of stability in the format of Ulam. Finally, by several examples we demonstrate applications of the main findings.
Topics & Concepts
ThermostatMathematicsUniquenessFixed-point theoremOperator (biology)Boundary value problemFixed pointOrdinary differential equationStability (learning theory)Banach fixed-point theoremApplied mathematicsPartial differential equationNonlinear systemFractional calculusMathematical analysisDifferential equationComputer scienceQuantum mechanicsPhysicsBiochemistryMachine learningTranscription factorThermodynamicsGeneRepressorChemistryFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems