Ad
related to: fractional calculus books pdf file size
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 ...
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 Coopmans approximation is a method for approximating a fractional-order integrator in a continuous process with constant space complexity.The most correct and accurate methods for calculating the fractional integral require a record of all previous history, and therefore would require a linear space complexity solution O(n), where n is the number of samples measured for the complete history.
Original file (814 × 1,154 pixels, file size: 48.82 MB, MIME type: application/pdf, 296 pages) This is a file from the Wikimedia Commons . Information from its description page there is shown below.
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.
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Pages for logged out editors learn more
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 .