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Fractal Fract
Volume 5
Issue 2
10.3390/fractalfract5020030
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Article

Approximate Controllability of Fully Nonlocal Stochastic Delay Control Problems Driven by Hybrid Noises

by
Lixu Yan
*,† and
Yongqiang Fu
†
School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Fractal Fract. 2021, 5(2), 30; https://doi.org/10.3390/fractalfract5020030
Submission received: 10 March 2021 / Revised: 7 April 2021 / Accepted: 8 April 2021 / Published: 12 April 2021
(This article belongs to the Special Issue Fractional and Anomalous Diffusions on Regular and Irregular Domains)
Versions Notes

Abstract

In this paper, a class of time-space fractional stochastic delay control problems with fractional noises and Poisson jumps in a bounded domain is considered. The proper function spaces and assumptions are proposed to discuss the existence of mild solutions. In particular, approximate strategy is used to obtain the existence of mild solutions for the problem with linear fractional noises; fixed point theorem is used to achieve the existence of mild solutions for the problem with nonlinear fractional noises. Finally, the approximate controllability of the problems with linear and nonlinear fractional noises is proved by the property of mild solutions.
Keywords: fully nonlocal derivative operator; mild solution; approximate controllability; fractional Brownian motion; Poisson jump fully nonlocal derivative operator; mild solution; approximate controllability; fractional Brownian motion; Poisson jump

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MDPI and ACS Style

Yan, L.; Fu, Y. Approximate Controllability of Fully Nonlocal Stochastic Delay Control Problems Driven by Hybrid Noises. Fractal Fract. 2021, 5, 30. https://doi.org/10.3390/fractalfract5020030

AMA Style

Yan L, Fu Y. Approximate Controllability of Fully Nonlocal Stochastic Delay Control Problems Driven by Hybrid Noises. Fractal and Fractional. 2021; 5(2):30. https://doi.org/10.3390/fractalfract5020030

Chicago/Turabian Style

Yan, Lixu, and Yongqiang Fu. 2021. "Approximate Controllability of Fully Nonlocal Stochastic Delay Control Problems Driven by Hybrid Noises" Fractal and Fractional 5, no. 2: 30. https://doi.org/10.3390/fractalfract5020030

APA Style

Yan, L., & Fu, Y. (2021). Approximate Controllability of Fully Nonlocal Stochastic Delay Control Problems Driven by Hybrid Noises. Fractal and Fractional, 5(2), 30. https://doi.org/10.3390/fractalfract5020030

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