What does fractional calculus mean?

fractional calculus

Word Rarity Rare

Frequency: Zipf frequency 2.94 in modern English

Syllables: frac-tion-al -cal-cu-lus
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Meaning

noun

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.

Uncountable

Example Sentences

"2000, Carl F. Lorenzo, Tom T. Hartley, Initialized Fractional Calculus, NASA, NASA/TP—2000-209943, page 12, The 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)."
"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."
"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."

Usage

Uncountable

Inflected Forms

fractional calculi (plural)

Phrases

fractional derivative fractional differential equation fractional Fourier transform fractional quantum mechanics fractional trigonometry fractional-order system

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