An analysis on asymptotic stability of Hilfer fractional stochastic evolution equations with infinite delay

Abstract

This article deals with the existence and asymptotic stability in the p-th moment of a mild solution for Hilfer fractional stochastic delay differential equations in Hilbert spaces. Our main results are obtained by fractional calculus, semigroup theory, stochastic analysis, and the Banach fixed point theorem. Further, a new set of sufficient conditions for existence and asymptotic stability in the p-th moment is derived with the help of a fixed point technique. Additionally, we provide an example to demonstrate the reliability of our results.

Keywords:

• Asymptotic stability
• Hilfer fractional derivative
• stochastic process
• mild solution
• fixed point technique

2010 MSC:

• 35B40
• 45M10
• 47H10
• 60G22
• 60G52

Author contributions

J. Pradeesh: Conceptualization, Methodology, Validation, Visualization, Writing – original draft. V. Vijayakumar: Conceptualization, Formal analysis, Resources, Supervision, Writing - original draft, Writing – Review & Editing.

Disclosure statement

This work does not have any conflicts of interest.

Data availability statement

Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

Additional information

Funding

There are no funders to report for this submission.