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Successive approximation and optimal controls on fractional neutral stochastic differential equations with Poisson jumps
Author(s) -
Rajivganthi C.,
Muthukumar P.,
Ganesh Priya B.
Publication year - 2015
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.2184
Subject(s) - mathematics , poisson distribution , stochastic differential equation , fractional calculus , operator (biology) , class (philosophy) , hilbert space , differential equation , set (abstract data type) , mathematical analysis , computer science , biochemistry , statistics , chemistry , repressor , artificial intelligence , transcription factor , gene , programming language
Summary The objective of this paper is to investigate the existence of mild solutions and optimal controls for a class of fractional neutral stochastic differential equations with Poisson jumps in Hilbert spaces. First, we establish a new set of sufficient conditions for the existence of mild solutions of the aforementioned fractional systems by using the successive approximation approach. The results are formulated and proved by using the fractional calculus, solution operator, and stochastic analysis techniques. The existence of optimal control pairs of system governed by fractional neutral stochastic differential equations with Poisson jumps is also presented. An example is given to illustrate the theory. Copyright © 2015 John Wiley & Sons, Ltd.