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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 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 mathematics, the Riemann–Liouville integral associates with a real function: another function I α f of the same kind for each value of the parameter α > 0.The integral is a manner of generalization of the repeated antiderivative of f in the sense that for positive integer values of α, I α f is an iterated antiderivative of f of order α.
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.
Pages in category "Fractional calculus" The following 18 pages are in this category, out of 18 total. This list may not reflect recent changes. ...
It covers research on fractional calculus, special functions, integral transforms, and some closely related areas of applied analysis. The journal is abstracted and indexed in Science Citation Index Expanded , Scopus , Current Contents /Physical, Chemical and Earth Sciences, Zentralblatt MATH , and Mathematical Reviews .
By applying a Laplace transform to the LTI system above, the transfer function becomes = () = = =For general orders and this is a non-rational transfer function. Non-rational transfer functions cannot be written as an expansion in a finite number of terms (e.g., a binomial expansion would have an infinite number of terms) and in this sense fractional orders systems can be said to have the ...
Specialized journal: Fractional Differential Equations (FDE) Specialized journal: Communications in Fractional Calculus (ISSN 2218-3892) Specialized journal: Journal of Fractional Calculus and Applications (JFCA) Lorenzo, Carl F.; Hartley, Tom T. (2002). "Initialized Fractional Calculus". Information Technology. Tech Briefs Media Group.