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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 ...
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.
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.
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.
Ximera is a massive open online course by Ohio State University on Coursera and YouTube. [1] The system was originally known as MOOCulus and Calculus One. [2] The course features over 25 hours of video and exercises. The instructor is Jim Fowler, an associate professor of mathematics at the Ohio State University. [3]
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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.
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