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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 ...
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.
The full title of the published work is "Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas nec irrationales quantitates moratur, et singulare pro illis calculi genus." In English, the full title can be translated as "A new method for maxima and minima, and for tangents, that is not hindered by fractional or irrational ...
Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "Fractional calculus" The following 18 pages are in this category, out of ...
The primary concept behind fractional calculus of sets is the characterization of fractional calculus elements using sets due to the plethora of fractional operators available. [3] [4] [5] This methodology originated from the development of the Fractional Newton-Raphson method [6] and subsequent related works. [7] [8] [9] [10]
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.
Linearity rules (+) = + () = ()Zero rule =; Product rule = = () (); In general, composition (or semigroup) rule is a desirable property, but is hard to achieve mathematically and hence is not always completely satisfied by each proposed operator; [3] this forms part of the decision making process on which one to choose:
Prabhakar function is a certain special function in mathematics introduced by the Indian mathematician Tilak Raj Prabhakar in a paper published in 1971. [1] The function is a three-parameter generalization of the well known two-parameter Mittag-Leffler function in mathematics.