Existence and approximate controllability of Hilfer fractional evolution equations with almost sectorial operators
Pallavi Bedi, Anoop Kumar, Thabet Abdeljawad, Zareen A. Khan, Aziz Khan
Abstract
Abstract In this article, we are concerned with the existence of mild solutions and approximate controllability of Hilfer fractional evolution equations with almost sectorial operators and nonlocal conditions. The existence results are obtained by first defining Green’s function and approximate controllability by specifying a suitable control function. These results are established with the help of Schauder’s fixed point theorem and theory of almost sectorial operators in a Banach space. An example is also presented for the demonstration of obtained results.
Topics & Concepts
ControllabilityMathematicsBanach spaceFixed-point theoremPartial differential equationOrdinary differential equationApplied mathematicsFunction (biology)Control functionFunctional analysisSchauder fixed point theoremMathematical analysisFixed pointBanach fixed-point theoremPure mathematicsDifferential equationControl (management)Picard–Lindelöf theoremComputer scienceBiologyChemistryArtificial intelligenceBiochemistryEvolutionary biologyGeneNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsDifferential Equations and Boundary Problems