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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 ...
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 QR code; Print/export Download as PDF; ... Pages in category "Fractional calculus" The following 18 pages are in this category, out of 18 total.
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.
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 applied mathematics and mathematical analysis, the fractal derivative or Hausdorff derivative is a non-Newtonian generalization of the derivative dealing with the measurement of fractals, defined in fractal geometry.
Calculus focuses on rates of change (within functions), such as accelerations, curves, and slopes. The development of calculus is credited to Archimedes, Bhaskara, Madhava of Sangamagrama, Gottfried Leibniz and Isaac Newton; lesser credit is given to Isaac Barrow, René Descartes, Pierre de Fermat, Christiaan Huygens, and John Wallis.
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