RESULTS ON HILFER FRACTIONAL STOCHASTIC SWITCHED DYNAMICAL SYSTEMS WITH IMPULSES: EXISTENCE AND OPTIMAL CONTROLS

Rajesh Dhayal (), Salah Boulaaras and Sulima Zubair
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Rajesh Dhayal: Department of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147004, India
Salah Boulaaras: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Sulima Zubair: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-15

Abstract: The objective of this paper is to consider a new class of Hilfer fractional stochastic switched dynamical systems under the influence of non-instantaneous impulses and the Rosenblatt process, where the abrupt changes occur suddenly at specific points and extend over finite time intervals. We proposed fractional optimal control strategies that minimize the cost function while considering both the stochastic dynamics of the systems and the intermittent switching between various modes. Using fractional calculus, the fixed-point method, and the Mittag-Leffler function, we established the existence of a unique mild solution for the proposed switched systems. Furthermore, by applying the Marzur lemma, we derived the optimal control results for the switched systems. Finally, we present an example to demonstrate the application of the obtained results.

Keywords: Stochastic Switched Systems; Hilfer Fractional Derivative; Rosenblatt Process; Impulses; Optimal Controls; Nonlinear Equations; Fractional Derivatives (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401383

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