A Generalization of Difference Models of the Bittner Operational Calculus-Reference-Cited by-同舟云学术

A Generalization of Difference Models of the Bittner Operational Calculus

Published:2019-12-01 Issue:4 Volume:219 Page:41-52
ISSN:2657-7291
Container-title:Scientific Journal of Polish Naval Academy
language:en
Short-container-title:

Author:

Wysocki Hubert¹^ORCID

Affiliation:

1. Polish Naval Academy , Faculty of Mechanical and Electrical Engineering , Śmidowicza 69 Str., 81-127 Gdynia , Poland

Abstract

Abstract In the paper, there has been constructed a discrete model of the non-classical Bittner operational calculus with a derivative understood as the operation S b {x(k)} := {x(k+n) − b(k)x(k)}, which is a generalization of the n th-order forward difference. It has also been pointed out that there is a possibility to generalize operational calculus models with backward and central differences of higher orders.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/sjpna-2019-0024

Reference10 articles.

1. [1] Bittner R., On certain axiomatics for the operational calculus, ‘Bull. Acad. Polon. Sci.’, Cl. III, 1959, 7(1), pp. 1–9.

2. [2] Bittner R., Operational calculus in linear spaces, ‘Studia Math.’, 1961, 20, pp. 1–18.10.4064/sm-20-1-1-18

3. [3] Bittner R., Algebraic and analytic properties of solutions of abstract differential equations, ‘Rozprawy Matematyczne’ [‘Dissertationes Math.’], 42, PWN, Warszawa 1964.

4. [4] Bittner R., Rachunek operatorów w przestrzeniach liniowych, PWN, Warszawa 1974 [Operational Calculus in Linear Spaces — available in Polish].

5. [5] Elaydi S., An Introduction to Difference Equations, Springer Sci. and Business Media, New York 2005.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. An Operational Calculus Model with the (m,n) - Symmetric Difference;Scientific Journal of Polish Naval Academy;2020-12-01