The averaging principle of Hilfer fractional stochastic delay differential equations with Poisson jumps | Zendy

Hamdy M. Ahmed | Zendy; Quanxin Zhu | Zendy

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The averaging principle of Hilfer fractional stochastic delay differential equations with Poisson jumps

Author(s) -

Hamdy M. Ahmed,

Quanxin Zhu

Publication year - 2020

Publication title -

applied mathematics letters

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.439

H-Index - 93

eISSN - 1873-5452

pISSN - 0893-9659

DOI - 10.1016/j.aml.2020.106755

Subject(s) - mathematics , poisson distribution , martingale (probability theory) , doob's martingale inequality , fractional calculus , stochastic differential equation , mathematical analysis , local martingale , statistics

This paper is concerned with Hilfer fractional stochastic delay differential equations with Poisson jumps. Under some assumptions, we obtain an averaging principle for the solution of the considered system. The required results are obtained based on fractional calculus, Doob’s martingale inequality and Cauchy–Schwarz inequality.

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