The Existence of Mild Solutions for Hilfer Fractional Stochastic Evolution Equations with Order μ∈(1,2)
Qien Li, Yong Zhou
Abstract
In this study, we investigate the existence of mild solutions for a class of Hilfer fractional stochastic evolution equations with order μ∈(1,2) and type ν∈[0,1]. We prove the existence of mild solutions of Hilfer fractional stochastic evolution equations when the semigroup is compact as well as noncompact. Our approach is based on the Schauder fixed point theorem, the Ascoli–Arzelà theorem and the Kuratowski measure of noncompactness. An example is also provided, to demonstrate the efficacy of this method.
Topics & Concepts
MathematicsFixed-point theoremSemigroupOrder (exchange)Schauder fixed point theoremApplied mathematicsType (biology)Class (philosophy)Fractional calculusMathematical analysisPicard–Lindelöf theoremComputer scienceEconomicsBiologyArtificial intelligenceFinanceEcologyNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsNonlinear Partial Differential Equations