Optimal control of fractional neutral stochastic differential equations with deviated argument governed by Poisson jumps and infinite delay. (23rd May 2019)

• Record Type: Journal Article
• Authors: Durga, N.; Muthukumar, P.
• Is Part Of: Optimal control applications and methods. Volume 40:Number 5(2019)
• Page Start: 880
• Page End: 899
• Publication Date: 2019-05-23
• Subjects: deviated argument -- existence of mild solutions -- fractional differential equations with infinite delay -- optimal control -- Poisson jumps; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2515
• Languages: English
• ISSNs: 0143-2087

Abstract

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.