{
  "id": "1602.01500",
  "version": "v1",
  "published": "2016-01-25T16:07:20.000Z",
  "updated": "2016-01-25T16:07:20.000Z",
  "title": "On Fractional q-Sturm--Liouville problems",
  "authors": [
    "Zeinab S. I. Mansour"
  ],
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we formulate a regular $q$-fractional Sturm--Liouville problem (qFSLP) which includes the left-sided Riemann--Liouville and the right-sided Caputo q-fractional derivatives of the same order $\\alpha$, $\\alpha\\in (0,1)$. The properties of the eigenvalues and the eigenfunctions are investigated. A $q$-fractional version of the Wronskian is defined and its relation to the simplicity of the eigenfunctions is verified. We use the fixed point theorem to introduce a sufficient condition on eigenvalues for the existence and uniqueness of the associated eigenfunctions when $\\alpha>1/2$. These results are a generalization of the integer regular $q$-Sturm--Liouville problem introduced by Annaby and Mansour in[1]. An example for a qFSLP whose eigenfunctions are little $q$-Jacobi polynomials is introduced.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-25T16:07:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional q-sturm-liouville problems",
      "eigenfunctions",
      "right-sided caputo q-fractional derivatives",
      "fractional sturm-liouville problem",
      "eigenvalues"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160201500M"
    }
  }
}