Scholarlink

Abstract <p> We study generalized (in the minimax sense) solutions of a Cauchy problem fora (path-dependent) Hamilton–Jacobi equation with fractional coinvariant derivatives undera right-end boundary condition for the case in which the Hamiltonian of the equation isa measurable function of the time variable. Theorems on the existence and uniqueness ofa minimax solution and a theorem on the continuous dependence of this solution on variations inthe Hamiltonian and the boundary functional are proved. The results are applied to the study ofa differential game for a dynamical system described by a differential equation with a Caputofractional derivative.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Generalized Solutions of Hamilton–Jacobi Equations with Fractional Coinvariant Derivatives and Time-Measurable Hamiltonian

  • 期刊论文

  • 发表日期：

    2025年11月1日

查看全文
  • M. I. Gomoyunov

摘要

Abstract

We study generalized (in the minimax sense) solutions of a Cauchy problem fora (path-dependent) Hamilton–Jacobi equation with fractional coinvariant derivatives undera right-end boundary condition for the case in which the Hamiltonian of the equation isa measurable function of the time variable. Theorems on the existence and uniqueness ofa minimax solution and a theorem on the continuous dependence of this solution on variations inthe Hamiltonian and the boundary functional are proved. The results are applied to the study ofa differential game for a dynamical system described by a differential equation with a Caputofractional derivative.