Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series. (4th November 2015)

• Record Type: Journal Article
• Authors: Tarasov, Vasily E.
• Other Names: Ohlberger Mario Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2015(2015)
• Publication Date: 2015-11-04
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2015/134842
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : New differences of integer orders, which are connected with derivatives of integer orders not approximately, are proposed. These differences are represented by infinite series. A characteristic property of the suggested differences is that its Fourier series transforms have a power-law form. We demonstrate that the proposed differences of integer orders n are directly connected with the derivatives ∂ n / ∂ x n . In contrast to the usual finite differences of integer orders, the suggested differences give the usual derivatives without approximation.