Multi-term time-fractional stochastic system with multiple delays in control

In the present paper, we study a multi-term time-fractional stochastic differential equation with multiple delays in control. We employ a general mild solution of the system, achieved by the generalization of the semigroup as a (α,γi)-resolvent family. An approach to transforming the controllability...

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2023-02, Vol.167, p.112979, Article 112979
Main Authors: Raheem, A., Afreen, A., Khatoon, A.
Format: Article
Language:English
Subjects:
Caputo fractional derivative
Controllability
Multi-term time-fractional system
Multiple delays
Stochastic system
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Summary:In the present paper, we study a multi-term time-fractional stochastic differential equation with multiple delays in control. We employ a general mild solution of the system, achieved by the generalization of the semigroup as a (α,γi)-resolvent family. An approach to transforming the controllability problem into a fixed point problem is developed to examine the controllability results. An example is given to illustrate the results. •We study a multi-term time-fractional stochastic system with several delays in control.•We proved the existence of a mild solution of the system.•We proved the approximate controllability of the system.•We showed that the system admits an optimal state-control pair.•An example is included to demonstrate the results.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2022.112979