Study a class of Hilfer fractional stochastic integrodifferential equations with Poisson jumps. Issue 6 (3rd December 2018)

• Record Type: Journal Article
• Authors: Balasubramaniam, P.; Saravanakumar, S.; Ratnavelu, K.
• Is Part Of: Stochastic analysis and applications. Volume 36:Issue 6(2018)
• Page Start: 1021
• Page End: 1036
• Publication Date: 2018-12-03
• Subjects: Hilfer fractional derivative -- stochastic fractional differential equations -- fixed point theorem -- mild solution -- nonlocal condition -- Poisson jumps; 74H20 -- 34A08 -- 58C30 -- 45J05 -- 65H10; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2018.1524303
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: In this article, we derive the sufficient conditions for the existence of mild solutions of Hilfer fractional stochastic integrodifferential equations with nonlocal conditions and Poisson jumps in Hilbert spaces. Results will be obtained in the p th mean square sense by using the fractional calculus, semigroup theory and stochastic analysis techniques. The article generalizes many of the existing results in the literature in terms of (1) Riemann–Liouville and Caputo derivatives are the special cases. (2) In the sense of p th mean square norm. (3) Stochastic integrodifferential with nonlocal conditions and Poisson jumps. A numerical example is provided to validate the obtained theoretical results.