{
  "id": "2106.15122",
  "version": "v1",
  "published": "2021-06-29T07:05:53.000Z",
  "updated": "2021-06-29T07:05:53.000Z",
  "title": "Approximate controllability of non-instantaneous impulsive fractional evolution equations of order $1<α<2$ with state-dependent delay in Banach spaces",
  "authors": [
    "S. Arora",
    "Manil T. Mohan",
    "J. Dabas"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2106.02939",
  "categories": [
    "math.OC"
  ],
  "abstract": "The current article examines the approximate controllability problem for non-instantaneous impulsive fractional evolution equations of order $1<\\alpha<2$ with state-dependent delay in separable reflexive Banach spaces. In order to establish sufficient conditions for the approximate controllability of our problem, we first formulate the linear-regulator problem and obtain the optimal control in feedback form. By using this optimal control, we deduce the approximate controllability of the linear fractional control system of order $1<\\alpha<2$. Further, we derive sufficient conditions for the approximate controllability of the nonlinear problem. Finally, we provide a concrete example to validate the efficiency of the derived results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-29T07:05:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K06",
      "34A12",
      "37L05",
      "93B05"
    ],
    "keywords": [
      "non-instantaneous impulsive fractional evolution equations",
      "approximate controllability",
      "state-dependent delay",
      "banach spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}