fractional calculus
From Wiktionary, the free dictionary
Noun
fractional calculus (countable and uncountable, plural fractional calculi)
- (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.
- 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).
- 2007, J. Sabatier, O. P. Agrawal, J. A. Tenreiro Machado, editors, Advances in Fractional Calculus, Springer, page xii:
- 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.
- 2008, Shantanu Das, Functional Fractional Calculus for System Identification and Controls, Springer, page 19:
- 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.
- 2000, Carl F. Lorenzo, Tom T. Hartley, Initialized Fractional Calculus, NASA, NASA/TP—2000-209943, page 12,
Related terms
- fractional derivative
- fractional differential equation
- fractional Fourier transform
- fractional quantum mechanics
- fractional trigonometry
Translations
branch of analysis
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See also
- fractional-order system
Further reading
Differintegral on Wikipedia.Wikipedia - Erdelyi–Kober operator on Wikipedia.Wikipedia
- Riemann–Liouville integral on Wikipedia.Wikipedia
- Weyl integral on Wikipedia.Wikipedia
- Mittag-Leffler function on Wikipedia.Wikipedia
- Fractional Fourier transform on Wikipedia.Wikipedia
- Fractional-order system on Wikipedia.Wikipedia
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