Optimal Control Problems for Hilfer Fractional Neutral Stochastic Evolution Hemivariational Inequalities

Abstract

In this paper, we concentrate on a control system with a non-local condition that is governed by a Hilfer fractional neutral stochastic evolution hemivariational inequality (HFNSEHVI). By using concepts of the generalized Clarke sub-differential and a fixed point theorem for multivalued maps, we first demonstrate adequate requirements for the existence of mild solutions to the concerned control system. Then, using limited Lagrange optimal systems, we demonstrate the existence of optimal state-control pairs that are regulated by an HFNSEHVI with a non-local condition. In order to demonstrate the existence of fixed points, the symmetric structure of the spaces and operators that we create is essential. Without considering the uniqueness of the control system’s solutions, the best control results are established. Lastly, an illustration is used to demonstrate the major result.

Hilfer Fractional Neutral Stochastic Differential Inclusions with Clarke’s Subdifferential Type and fBm: Approximate Boundary Controllability

“…Kavitha et al [33] discussed the results on the approximate controllability of Sobolev-type fractional neutral differential inclusions of the Clarke subdifferential type. Sivasankar et al [34] studied the optimal control problems for Hilfer fractional neutral stochastic evolution hemivariational inequalities.…”

New Study on the Controllability of Non-Instantaneous Impulsive Hilfer Fractional Neutral Stochastic Evolution Equations with Non-Dense Domain

“…SDEs capture some occurrences in a way that makes them mathematically unpredictable. For an extensive overview of SDEs and their uses, one can refer to [26][27][28][29][30][31]. All physical systems evolving with respect to time experience abrupt changes called impulses.…”

قابلية الحل للسيطرة الامثلية الحدودية الرباعية المستمرة التقليدية المسيطر بالنظام الرباعي المكافيء

“…Optimal control problems play an important role in many practical applications, such as in medicine 1 , aircraft 2 , economics 3 , robotics 4 , weather conditions 5 and many other scientific fields. There are two types of optimal control problems; the classical and the relax type, each one is either continuous or discrete, also each one of them is dominated either by ODEqs [6][7][8] or by PDEqs 9 .…”

“…In each type of these classical continuous boundary optimal control problems, the problem consists of; an initial or a boundary value problem (the dominating eqs. ), the objective (cost) function of the classical continuous control vector, and the 2024, 21 (6): 2093-2103 https://doi.org /10.21123/bsj.2023.8690 P-ISSN: 2078-8665 -E-ISSN: 2411 Baghdad Science Journal constraints on the state vector (equality and inequality state constraints). The study in each one of these problems included; the state and proof for the existence theorem of a continuous classical boundary optimal control that satisfies the state constraints under suitable conditions, the derivation of the mathematical formulation of the adjoint eqs.…”