Solvability and optimal controls of non-instantaneous impulsive stochastic neutral integro-differential equation driven by fractional Brownian motion

Rajesh Dhayal; Muslim Malik; Syed Abbas; Rajesh Dhayal; Muslim Malik; Syed Abbas

doi:10.3934/math.2019.3.663

AIMS Mathematics

2019, Volume 4, Issue 3: 663-683. doi: 10.3934/math.2019.3.663

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Solvability and optimal controls of non-instantaneous impulsive stochastic neutral integro-differential equation driven by fractional Brownian motion

School of Basic Sciences, Indian Institute of Technology Mandi, Kamand (H.P.) - 175 005, India

Received: 25 March 2019 Accepted: 20 May 2019 Published: 17 June 2019
MSC : 34K45, 60G22, 65C30, 93E20

In this manuscript, a new class of non-instantaneous impulsive stochastic neutral integrodi fferential equation driven by fractional Brownian motion (fBm, in short) with state-dependent delay and their stochastic optimal control problem is studied. We utilize the theory of the resolvent operator and a fixed point technique to present the solvability of the stochastic system. Then, the existence of optimal controls is discussed for the proposed stochastic system. Finally, an example is offered to demonstrate the obtained theoretical results.
- stochastic neutral integro-differential equation,
- optimal controls,
- state-dependent delay,
- fractional Brownian motion,
- non-instantaneous impulses
Citation: Rajesh Dhayal, Muslim Malik, Syed Abbas. Solvability and optimal controls of non-instantaneous impulsive stochastic neutral integro-differential equation driven by fractional Brownian motion[J]. AIMS Mathematics, 2019, 4(3): 663-683. doi: 10.3934/math.2019.3.663

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Abstract

In this manuscript, a new class of non-instantaneous impulsive stochastic neutral integrodi fferential equation driven by fractional Brownian motion (fBm, in short) with state-dependent delay and their stochastic optimal control problem is studied. We utilize the theory of the resolvent operator and a fixed point technique to present the solvability of the stochastic system. Then, the existence of optimal controls is discussed for the proposed stochastic system. Finally, an example is offered to demonstrate the obtained theoretical results.

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