<abstract xmlns="http://www.w3.org/1999/xhtml">In the paper, there has been constructed such a non-classical Bittner operational calculus model, in which the derivative is understood as a central difference <italic>Dn</italic>{<italic>x(k)</italic>}:= {<italic>x(k+n</italic>)–<italic>x(k-n)</italic>}. The discussed model has been generalized by considering the operation Dn,b{<italic>x(k)</italic>}:= {<italic>x(k+n</italic>)–<italic>bx(k-n)</italic>}, where b∈𝕔\{0}. In the <italic>D</italic>1-difference model exponential-trigonometric and hyperbolic Fibonacci sequences have been introduced.</abstract>

In the paper, there has been constructed such a non-classical Bittner operational calculus model, in which the derivative is understood as a central difference Dn{x(k)}:= {x(k+n)–x(k-n)}. The discussed model has been generalized by considering the operation Dn,b{x(k)}:= {x(k+n)–bx(k-n)}, where b∈𝕔\{0}. In the D1-difference model exponential-trigonometric and hyperbolic Fibonacci sequences have been introduced.

An operational calculus model for the central difference and exponential-trigonometric and hyperbolic fibonacci sequences

Polish Naval Academy, Faculty of Mechanical and Electrical Engineering

Maritime Technical Journal

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In the paper, there has been constructed such a non-classical Bittner operational calculus model, in which the derivative is understood as a central difference...

An operational calculus model for the central difference and exponential-trigonometric and hyperbolic fibonacci sequences

Published Online: Sep 30, 2018

Page range: 39 - 62

Received: Jun 14, 2018

Accepted: Sep 20, 2018

DOI: https://doi.org/10.2478/sjpna-2018-0018

Keywords
operational calculus, derivative, integrals, limit conditions, central difference, Fibonacci sequences

© 2018 Hubert Wysocki, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

An operational calculus model for the central difference and exponential-trigonometric and hyperbolic fibonacci sequences

Published Online: Sep 30, 2018

Page range: 39 - 62

Received: Jun 14, 2018

Accepted: Sep 20, 2018

DOI: https://doi.org/10.2478/sjpna-2018-0018

Keywordsoperational calculus, derivative, integrals, limit conditions, central difference, Fibonacci sequences

© 2018 Hubert Wysocki, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
operational calculus, derivative, integrals, limit conditions, central difference, Fibonacci sequences