"fractional calculus" meaning in English

{
  "forms": [
    {
      "form": "fractional calculi",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "~",
        "2": "fractional calculi"
      },
      "expansion": "fractional calculus (countable and uncountable, plural fractional calculi)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "2000, Carl F. Lorenzo, Tom T. Hartley, Initialized Fractional Calculus, NASA, NASA/TP—2000-209943, page 12,\nThe paper presents the definition sets required for initialized fractional calculi. Two underlying bases have been used, the Riemann-Liouville based fractional calculus and the Grünwald based functional calculus (by reference)."
        },
        {
          "ref": "2007, J. Sabatier, O. P. Agrawal, J. A. Tenreiro Machado, editors, Advances in Fractional Calculus, Springer, page xii",
          "text": "One of the major advantages of fractional calculus is that it can be considered as a superset of integer-order calculus. Thus fractional calculus has the potential to accomplish what integer-order calculus cannot. We believe that many of the great future developments will come from the applications of fractional calculus to different fields.",
          "type": "quotation"
        },
        {
          "ref": "2008, Shantanu Das, Functional Fractional Calculus for System Identification and Controls, Springer, page 19",
          "text": "This chapter presents a number of functions that have been found to be useful in providing solutions to the problems of fractional calculus. […]The Mittag-Leffler function is the basis function to functional calculus, as the exponential function is to the integer-order calculus.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The branch of mathematics that studies generalisations of calculus to allow noninteger (i.e., real or complex) powers of the differentiation operator D and the integration operator J; (countable) any one of said generalisations of calculus."
      ],
      "id": "en-fractional_calculus-en-noun-PGepGELf",
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "calculus",
          "calculus"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis, uncountable) The branch of mathematics that studies generalisations of calculus to allow noninteger (i.e., real or complex) powers of the differentiation operator D and the integration operator J; (countable) any one of said generalisations of calculus."
      ],
      "related": [
        {
          "word": "fractional derivative"
        },
        {
          "word": "fractional differential equation"
        },
        {
          "word": "fractional Fourier transform"
        },
        {
          "word": "fractional quantum mechanics"
        },
        {
          "word": "fractional trigonometry"
        },
        {
          "word": "fractional-order system"
        }
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "fr",
          "lang": "French",
          "sense": "branch of analysis",
          "tags": [
            "feminine"
          ],
          "word": "analyse fractionnaire"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "branch of analysis",
          "tags": [
            "feminine"
          ],
          "word": "fraktionale Infinitesimalrechnung"
        },
        {
          "code": "it",
          "lang": "Italian",
          "sense": "branch of analysis",
          "tags": [
            "masculine"
          ],
          "word": "calcolo frazionario"
        },
        {
          "code": "pt",
          "lang": "Portughese",
          "sense": "branch of analysis",
          "tags": [
            "masculine"
          ],
          "word": "cálculo fracionário"
        },
        {
          "code": "pt",
          "lang": "Portughese",
          "sense": "branch of analysis",
          "tags": [
            "masculine"
          ],
          "word": "cálculo de ordem não inteira"
        },
        {
          "code": "es",
          "lang": "Spanish",
          "sense": "branch of analysis",
          "tags": [
            "masculine"
          ],
          "word": "cálculo fraccional"
        }
      ],
      "wikipedia": [
        "fractional calculus"
      ]
    }
  ],
  "word": "fractional calculus"
}

{
  "forms": [
    {
      "form": "fractional calculi",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "~",
        "2": "fractional calculi"
      },
      "expansion": "fractional calculus (countable and uncountable, plural fractional calculi)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "fractional derivative"
    },
    {
      "word": "fractional differential equation"
    },
    {
      "word": "fractional Fourier transform"
    },
    {
      "word": "fractional quantum mechanics"
    },
    {
      "word": "fractional trigonometry"
    },
    {
      "word": "fractional-order system"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "English uncountable nouns",
        "en:Mathematical analysis"
      ],
      "examples": [
        {
          "text": "2000, Carl F. Lorenzo, Tom T. Hartley, Initialized Fractional Calculus, NASA, NASA/TP—2000-209943, page 12,\nThe paper presents the definition sets required for initialized fractional calculi. Two underlying bases have been used, the Riemann-Liouville based fractional calculus and the Grünwald based functional calculus (by reference)."
        },
        {
          "ref": "2007, J. Sabatier, O. P. Agrawal, J. A. Tenreiro Machado, editors, Advances in Fractional Calculus, Springer, page xii",
          "text": "One of the major advantages of fractional calculus is that it can be considered as a superset of integer-order calculus. Thus fractional calculus has the potential to accomplish what integer-order calculus cannot. We believe that many of the great future developments will come from the applications of fractional calculus to different fields.",
          "type": "quotation"
        },
        {
          "ref": "2008, Shantanu Das, Functional Fractional Calculus for System Identification and Controls, Springer, page 19",
          "text": "This chapter presents a number of functions that have been found to be useful in providing solutions to the problems of fractional calculus. […]The Mittag-Leffler function is the basis function to functional calculus, as the exponential function is to the integer-order calculus.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The branch of mathematics that studies generalisations of calculus to allow noninteger (i.e., real or complex) powers of the differentiation operator D and the integration operator J; (countable) any one of said generalisations of calculus."
      ],
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "calculus",
          "calculus"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis, uncountable) The branch of mathematics that studies generalisations of calculus to allow noninteger (i.e., real or complex) powers of the differentiation operator D and the integration operator J; (countable) any one of said generalisations of calculus."
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "fractional calculus"
      ]
    }
  ],
  "translations": [
    {
      "code": "fr",
      "lang": "French",
      "sense": "branch of analysis",
      "tags": [
        "feminine"
      ],
      "word": "analyse fractionnaire"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "branch of analysis",
      "tags": [
        "feminine"
      ],
      "word": "fraktionale Infinitesimalrechnung"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "branch of analysis",
      "tags": [
        "masculine"
      ],
      "word": "calcolo frazionario"
    },
    {
      "code": "pt",
      "lang": "Portughese",
      "sense": "branch of analysis",
      "tags": [
        "masculine"
      ],
      "word": "cálculo fracionário"
    },
    {
      "code": "pt",
      "lang": "Portughese",
      "sense": "branch of analysis",
      "tags": [
        "masculine"
      ],
      "word": "cálculo de ordem não inteira"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "branch of analysis",
      "tags": [
        "masculine"
      ],
      "word": "cálculo fraccional"
    }
  ],
  "word": "fractional calculus"
}