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Optimal control of fractional neutral stochastic differential equations with deviated argument governed by Poisson jumps and infinite delay
Author(s) -
Durga N.,
Muthukumar P.
Publication year - 2019
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2515
Subject(s) - mathematics , fractional calculus , hilbert space , stochastic partial differential equation , stochastic differential equation , fixed point theorem , operator (biology) , stochastic control , mathematical analysis , poisson distribution , optimal control , differential equation , mathematical optimization , biochemistry , chemistry , statistics , repressor , transcription factor , gene
Summary In this work, the optimal control for a class of fractional neutral stochastic differential equations with deviated arguments driven by infinite delay and Poisson jumps is studied in Hilbert space involving the Caputo fractional derivative. The sufficient conditions for the existence of mild solution results are formulated and proved by the virtue of fractional calculus, characteristic solution operator, fixed‐point theorem, and stochastic analysis techniques. Furthermore, the existence of optimal control of the proposed problem is presented by using Balder's theorem. Finally, the obtained theoretical results are applied to the fractional stochastic partial differential equations and a stochastic river pollution model.