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Fractional calculus was introduced in one of Niels Henrik Abel's early papers [3] where all the elements can be found: the idea of fractional-order integration and differentiation, the mutually inverse relationship between them, the understanding that fractional-order differentiation and integration can be considered as the same generalized ...
Agnieszka Barbara Malinowska is a Polish mathematician known for her research and books on fractional calculus and the fractional calculus of variations. She is an associate professor of mathematics, in the faculty of computer science of Bialystok University of Technology. [1] [2]
In mathematics, the Grünwald–Letnikov derivative is a basic extension of the derivative in fractional calculus that allows one to take the derivative a non-integer number of times. It was introduced by Anton Karl Grünwald (1838–1920) from Prague , in 1867, and by Aleksey Vasilievich Letnikov (1837–1888) in Moscow in 1868.
In fractional calculus, these formulae can be used to construct a differintegral, allowing one to differentiate or integrate a fractional number of times. Differentiating a fractional number of times can be accomplished by fractional integration, then differentiating the result.
Working with a properly initialized differ integral is the subject of initialized fractional calculus. If the differ integral is initialized properly, then the hoped-for composition law holds. The problem is that in differentiation, information is lost, as with C in the first equation.
Fractional Calculus and Applied Analysis is a peer-reviewed mathematics journal published by Walter de Gruyter. It covers research on fractional calculus , special functions , integral transforms , and some closely related areas of applied analysis .
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Igor Podlubny's collection of related books, articles, links, software, etc. Podlubny, I. (2002). "Geometric and physical interpretation of fractional integration and fractional differentiation" (PDF). Fractional Calculus and Applied Analysis. 5 (4): 367– 386. arXiv: math.CA/0110241. Bibcode:2001math.....10241P. Archived from the original ...