See fractional calculus on Wiktionary
{
"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": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Italian translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Portuguese translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Spanish translations",
"parents": [],
"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": "quote"
},
{
"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": "quote"
}
],
"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": "Portuguese",
"sense": "branch of analysis",
"tags": [
"masculine"
],
"word": "cálculo fracionário"
},
{
"code": "pt",
"lang": "Portuguese",
"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",
"Entries with translation boxes",
"Pages with 1 entry",
"Pages with entries",
"Terms with French translations",
"Terms with German translations",
"Terms with Italian translations",
"Terms with Portuguese translations",
"Terms with Spanish translations",
"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": "quote"
},
{
"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": "quote"
}
],
"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": "Portuguese",
"sense": "branch of analysis",
"tags": [
"masculine"
],
"word": "cálculo fracionário"
},
{
"code": "pt",
"lang": "Portuguese",
"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"
}
Download raw JSONL data for fractional calculus meaning in All languages combined (3.8kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-01-31 from the enwiktionary dump dated 2025-01-20 using wiktextract (bcd5c38 and 9dbd323). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.