Null controllability of Hilfer fractional stochastic differential equations with nonlocal conditions

Dimplekumar Chalishajar; K. Ravikumar; K. Ramkumar; A. Anguraj

doi:10.3934/naco.2022029

Article Contents

2024, Volume 14, Issue 2: 322-338. Doi: 10.3934/naco.2022029

This issue Previous Article Consistency of equilibrium stacks in finite uniform approximation of a noncooperative game played with staircase-function strategies Next Article Stochastic DDM with regime–switching process

Null controllability of Hilfer fractional stochastic differential equations with nonlocal conditions

1.
Department of Applied Mathematics, Virginia Military Institute, Lexington, VA 24450, USA
2.
Department of Mathematics, PSG College of Arts & Science, Coimbatore, 641 046, India

^*Corresponding author: Dimplekumar Chalishajar
^*Corresponding author: Dimplekumar Chalishajar

Received: June 2022

Revised: August 2022

Early access: September 28, 2022

Published online: September 28, 2022

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Abstract

This paper assesses a class of nonlocal Hilfer fractional stochastic differential equations (NHFSDEs) governed by fractional Brownian motion (fBm). New sufficient condition of exact null controllability for this stochastic setting has been investigated using fractional calculus, fixed point theory and a theory of resolvent operator. The derived result is new because it generalizes several of previously published results. However, the obtained results are proven by an illustration using stochastic partial differential equations to demonstrate the present application characteristic of null controllability. A filter example is demonstrated to make use of resolvent operator in a practical way.

Keywords:

Hilfer fractional stochastic differential equation,
fractional Brownian motion,
Poisson jump,
null controllability,
nonlocal conditions.

Mathematics Subject Classification: 26A33, 34A12, 34A08, 93B05.

Citation:

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Figure 1. Filter System.

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