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<p>This paper studies mild solutions and optimal control for Sobolev-type Hilfer–Katugampola fractional neutral stochastic evolution hemivariational inequalities with nonlocal initial conditions, fractional Brownian motion, and Clarke sub-differentials. Using semigroup theory, properties of the Clarke sub-differential, and fixed point methods for multivalued maps, we establish the existence of mild solutions. Furthermore, by employing a restricted Lagrange optimization framework, we derive optimal state–control pairs without assuming uniqueness. A numerical example illustrates the theoretical results.</p>

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Existence and regulation analysis for Hilfer–Katugampola fractional neutral hemivariational dynamics with nonlocal initialization and fractional noise

  • 期刊论文

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  • 发表日期：

    2025年12月5日

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  • A. M. Sayed Ahmed

摘要

This paper studies mild solutions and optimal control for Sobolev-type Hilfer–Katugampola fractional neutral stochastic evolution hemivariational inequalities with nonlocal initial conditions, fractional Brownian motion, and Clarke sub-differentials. Using semigroup theory, properties of the Clarke sub-differential, and fixed point methods for multivalued maps, we establish the existence of mild solutions. Furthermore, by employing a restricted Lagrange optimization framework, we derive optimal state–control pairs without assuming uniqueness. A numerical example illustrates the theoretical results.