{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "BH5TK7DC2X"
    },
    {
      "field": "uses",
      "target": "QRGSRA0CYV"
    }
  ],
  "body": "\n## Summary\n\nThe Caputo fractional derivative of order $\\alpha$ first differentiates a function $n = \\ceil{\\alpha}$ times and then applies the [[Riemann–Liouville integral|JTKCZ44NN3]] of order $n - \\alpha$.\nThis order of operations is the reverse of the Riemann–Liouville derivative.\nIts main advantage is that the derivative of a constant is zero, and fractional differential equations with it take ordinary initial values $f(a), f'(a), \\dots$.\nIt is a standard tool of [[fractional calculus|T73XK15SA2]] in applied models.\n\n## Explanations\n\n### L1 human\n\nTo take a derivative of order $1/2$, the Caputo rule takes one ordinary derivative and then a half integral.\nBecause the ordinary derivative comes first, constants are killed, just as in ordinary calculus.\nFor example, with lower terminal $0$, the Caputo derivative of order $1/2$ of $x$ is the half integral of $1$, which is $2\\sqrt{x/\\pi}$.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "26A33"
    ],
    "name": "Caputo fractional derivative",
    "same_as": {
      "wikidata": "Q130213521",
      "wikipedia": "Caputo fractional derivative"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Caputo_fractional_derivative"
      }
    ],
    "tag": "6VMGQYF8RW"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/6VMGQYF8RW/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/6VMGQYF8RW.md",
  "msc": [
    "26A33"
  ],
  "name": "Caputo fractional derivative",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/6VM/6VMGQYF8RW.md",
  "status": null,
  "tag": "6VMGQYF8RW",
  "uri": "m2://6VMGQYF8RW",
  "url": "https://math2.tamnd.com/wiki/caputo-fractional-derivative/",
  "writing": {
    "tag": "6VMGQYF8RW",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}