<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced <italic>normalized finite fractional difference </italic>is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated with the introduction of a <italic>perfect finite fractional difference </italic>and, in particular, a powerful <italic>adaptive finite fractional difference</italic>, whose excellent performance is illustrated in simulation examples.</p></abstract>

This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced normalized finite fractional difference is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated with the introduction of a perfect finite fractional difference and, in particular, a powerful adaptive finite fractional difference, whose excellent performance is illustrated in simulation examples.

Normalized finite fractional differences: Computational and accuracy breakthroughs

Institute of Control and Computer Engineering Opole University of Technology, ul. Sosnkowskiego 31, 45-272 Opole, Poland

International Journal of Applied Mathematics and Computer Science

This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced normalized finite...

Normalized finite fractional differences: Computational and accuracy breakthroughs

Published Online: Dec 28, 2012

Page range: 907 - 919

DOI: https://doi.org/10.2478/v10006-012-0067-9

This content is open access.