{
  "id": "1807.10105",
  "version": "v1",
  "published": "2018-07-26T13:13:27.000Z",
  "updated": "2018-07-26T13:13:27.000Z",
  "title": "Global Existence and Ulam--Hyers Stability for $ψ$--Hilfer Fractional Differential Equations",
  "authors": [
    "Kishor D. Kucche",
    "Jyoti P. Kharade"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving $\\psi$-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the the weighted space of functions. The Ulam-Hyers and Ulam-Hyers-Rassias stability of Cauchy--type problem is investigated via successive approximation method. Further, we investigate the dependence of solutions on the initial conditions and uniqueness via $\\epsilon$-approximated solution. An example is provided to illustrate the results we obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-26T13:13:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilfer fractional differential equations",
      "global existence",
      "ulam-hyers stability",
      "cauchy-type problem",
      "nonlinear differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}