Abstract
In this paper, we analyse the approximate controllability of Hilfer fractional stochastic differential systems of order in Hilbert spaces. The primary findings are carried out by using fractional calculus, stochastic analysis theory, cosine family, and Schauder's fixed point theorem. In particular, we draw a new set of sufficient conditions for the approximate controllability of Hilfer fractional stochastic differential equations of order
under the assumption that the corresponding linear system is approximately controllable. In the end, an example is provided to illustrate the derived theory.
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No potential conflict of interest was reported by the author(s).
Additional information
Notes on contributors
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J. Pradeesh
J. Pradeesh received B.Sc, and M.Sc, degrees in Mathematics from the Bharathiar University, Coimbatore, Tamil Nadu, India in 2020, and 2022, respectively. Now, he is pursuing his Ph.D. degree under the guidance of Prof. V. Vijayakumar at the Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India. His current research interests include Fractional Calculus, Dynamical systems, Stability analysis, and Control theory. To his credit, he has published 6 papers in reputed scientific journals.
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V. Vijayakumar
Dr. V. Vijayakumar received B.Sc, M.Sc, M.Phil, and Ph.D. degrees in Mathematics from the Bharathiar University, Coimbatore, Tamil Nadu, India in 2002, 2004, 2006, and 2016, respectively. He was a Lecturer with the Department of Mathematics, Sri Nandhanam College of Engineering and Technology, Tirupattur, Vellore, Tamil Nadu, India, from 2006 to 2007. He was an Assistant Professor and an Associate Professor with the Department of Mathematics, Info Institute of Engineering, Coimbatore, Tamil Nadu, India, from 2007 to 2019. Since 2019, he has been an Assistant Professor at Vellore Institute of Technology, Vellore, Tamil Nadu, India. His current research interests include Fractional Calculus, Dynamical Systems, Control Theory, and Neural Networks. To his credit, he has published more than 175 papers in reputed scientific journals. He is listed as TOP 2% Scientists in the World (All Fields) by a survey conducted by Elsevier BV and Stanford University, based on the citations, h-index, and co-authorship adjusted hm-index, for the years 2020, 2021 and 2022.