Existence of mild solutions for impulsive neutral Hilfer fractional evolution equations
Pallavi Bedi, Anoop Kumar, Thabet Abdeljawad, Aziz Khan
Abstract
Abstract In this paper, we investigate the existence of mild solutions for neutral Hilfer fractional evolution equations with noninstantaneous impulsive conditions in a Banach space. We obtain the existence results by applying the theory of resolvent operator functions, Hausdorff measure of noncompactness, and Sadovskii’s fixed point theorem. We also present an example to show the validity of obtained results.
Topics & Concepts
MathematicsResolventBanach spaceFixed-point theoremOrdinary differential equationPartial differential equationHausdorff measureMathematical analysisFixed pointC0-semigroupHausdorff spaceOperator (biology)Fractional calculusApplied mathematicsPure mathematicsDifferential equationHausdorff dimensionChemistryBiochemistryRepressorGeneTranscription factorNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsFixed Point Theorems Analysis