<p>In this article, we investigate a control system governed by a class of Hilfer fractional stochastic integrodifferential evolution hemivariational inequalities with mixed fractional Brownian motion. Our analysis draws on the concepts from fractional calculus, cosine families, stochastic analysis theory, fractional Brownian motion, and fixed-point theorems. Initially, we establish the existence of a mild solution for the proposed system by applying properties of the Wiener process and fractional Brownian motion, generalized Clarke’s subdifferential, and the fixed-point theorem for multivalued maps. Additionally, we develop and validate a new set of sufficient conditions for both the existence of solutions and the approximate controllability of Hilfer fractional nonlinear stochastic differential systems. These conditions assume that the linear part of the system is approximately controllable. An illustrative case is included at the end to validate the theoretical findings.</p>

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Results Concerning to Existence and Controllability of Hilfer Fractional Stochastic Integrodifferential Evolution Hemivariational Inequalities of Order \(1<\mu <2\) with Mixed fBm

  • J. Pradeesh,
  • V. Vijayakumar

摘要

In this article, we investigate a control system governed by a class of Hilfer fractional stochastic integrodifferential evolution hemivariational inequalities with mixed fractional Brownian motion. Our analysis draws on the concepts from fractional calculus, cosine families, stochastic analysis theory, fractional Brownian motion, and fixed-point theorems. Initially, we establish the existence of a mild solution for the proposed system by applying properties of the Wiener process and fractional Brownian motion, generalized Clarke’s subdifferential, and the fixed-point theorem for multivalued maps. Additionally, we develop and validate a new set of sufficient conditions for both the existence of solutions and the approximate controllability of Hilfer fractional nonlinear stochastic differential systems. These conditions assume that the linear part of the system is approximately controllable. An illustrative case is included at the end to validate the theoretical findings.