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Discussion on Existence of Mild Solutions for Hilfer Fractional Neutral Stochastic Evolution Equations Via Almost Sectorial Operators with Delay

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Abstract

In this paper, we formulate a new set of sufficient conditions for the existence of mild solutions for Hilfer fractional neutral stochastic evolution equations via almost sectorial operators with delay. The primary results are obtained from the properties of fractional calculus, stochastic analysis theory, the measure of noncompactness, and the fixed point technique. Firstly, we demonstrate the existence of mild solutions for Hilfer fractional neutral stochastic evolution equations via an almost sectorial operator with delay by using the Mönch fixed point theorem. The main result is finally demonstrated using an example.

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Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, 632 014, India

    S. Sivasankar & R. Udhayakumar

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  1. S. Sivasankar
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  2. R. Udhayakumar
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Contributions

Conceptualisation, S. Sivasankar (S.S)., R. Udhayakumar (R.U).; methodology, S.S.; validation, S.S., R.U.; formal analysis, S.S.; investigation, R.U.; resources, S.S.; writing original draft preparation, S.S.; writing review and editing, R.U., visualization, R.U.; supervision, R.U.; project administration, R.U. All authors have read and agreed to the published version of the manuscript.

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Correspondence to R. Udhayakumar.

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Sivasankar, S., Udhayakumar, R. Discussion on Existence of Mild Solutions for Hilfer Fractional Neutral Stochastic Evolution Equations Via Almost Sectorial Operators with Delay. Qual. Theory Dyn. Syst. 22, 67 (2023). https://doi.org/10.1007/s12346-023-00773-4

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