Non-instantaneous impulsive Hilfer fractional stochastic differential equations driven by fractional Brownian motion. Issue 3 (4th May 2021)

• Record Type: Journal Article
• Authors: Saravanakumar, S.; Balasubramaniam, P.
• Is Part Of: Stochastic analysis and applications. Volume 39:Issue 3(2021)
• Page Start: 549
• Page End: 566
• Publication Date: 2021-05-04
• Subjects: Existence of solution -- stochastic differential equations -- semigroup theory -- fixed point theorem -- fractional Brownian motion; 26A33 -- 34A12 -- 34A37 -- 34A08 -- 60H10; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2020.1815545
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: The aim of this manuscript is to analyze the existence of mild solution of non-instantaneous impulsive Hilfer fractional stochastic differential equations (NIHFSDEs) driven by fractional Brownian motion (fBm). Sufficient conditions for a class of NIHFSDEs of order 0 < β < 1 and of type 0 ≤ α ≤ 1 driven by fBm is derived with the help of fractional calculus, stochastic theory, fixed point theorem and semigroup theory. M ö nch fixed point theorem (FPT) is adopted to prove the existence of solution. In addition, a numerical example is provided to validate the theoretical result.