{
  "id": "2011.11306",
  "version": "v1",
  "published": "2020-11-23T10:06:17.000Z",
  "updated": "2020-11-23T10:06:17.000Z",
  "title": "Minimax Solutions of Hamilton--Jacobi Equations with Fractional Coinvariant Derivatives",
  "authors": [
    "Mikhail Gomoyunov"
  ],
  "categories": [
    "math.OC",
    "math.AP"
  ],
  "abstract": "We consider a Cauchy problem for a Hamilton--Jacobi equation with coinvariant derivatives of an order $\\alpha \\in (0, 1)$. Such problems arise naturally in optimal control problems for dynamical systems which evolution is described by ordinary differential equations with the Caputo fractional derivatives of the order $\\alpha$. We propose a notion of a generalized in the minimax sense solution of the considered problem. We prove that a minimax solution exists, is unique, and is consistent with a classical solution of this problem. In particular, we give a special attention to the proof of a comparison principle, which requires construction of a suitable Lyapunov--Krasovskii functional.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-23T10:06:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35F21",
      "35D99",
      "26A33"
    ],
    "keywords": [
      "fractional coinvariant derivatives",
      "hamilton-jacobi equation",
      "minimax solution",
      "optimal control problems",
      "minimax sense solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}