Study a class of Hilfer fractional stochastic integrodifferential equations with Poisson jumps

Document Type

Article

Publication Date

1-1-2018

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 pth 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 pth mean square norm. (3) Stochastic integrodifferential with nonlocal conditions and Poisson jumps. A numerical example is provided to validate the obtained theoretical results.

Keywords

Hilfer fractional derivative, stochastic fractional differential equations, fixed point theorem, mild solution, nonlocal condition, Poisson jumps

Divisions

MathematicalSciences

Funders

Fundamental Research Grant Scheme (FRGS) MoHE Grant (No. FP051-2016), University of Malaya, Malaysia,DST-SERB (MATRICS), New Delhi, Govt. of India, under file No. MTR/2017/001011

Publication Title

Stochastic Analysis and Applications

Volume

36

Issue

6

Publisher

Taylor & Francis

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