Search results
Results from the WOW.Com Content Network
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 ...
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]
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 ...
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.
Kiryakova won the 1996 Academic Prize for Mathematical Sciences of Bulgarian Academy of Sciences. [1] In 2012, at the 5th Symposium on Fractional Differentiation and its Applications, she was given the FDA Dissemination Award, for her "dissemination of fractional calculus among the scientific community, industry and society" over the previous five years.
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:
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.
In geometric calculus, the geometric derivative satisfies a weaker form of the Leibniz (product) rule. It specializes the Fréchet derivative to the objects of geometric algebra. Geometric calculus is a powerful formalism that has been shown to encompass the similar frameworks of differential forms and differential geometry. [1]