<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains at least one mesh consisting of branches only with an ideal supercapacitor and voltage sources or at least one node with branches with supercoils.</p></abstract>

A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains at least one mesh consisting of branches only with an ideal supercapacitor and voltage sources or at least one node with branches with supercoils.

Singular fractional linear systems and electrical circuits

Faculty of Electrical Engineering, Białystok Technical University, ul. Wiejska 45D, 15-351 Białystok, Poland

International Journal of Applied Mathematics and Computer Science

{"article-title":"Singular fractional linear systems and electrical circuits"}

A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the...

Singular fractional linear systems and electrical circuits

Published Online: Jun 22, 2011

Page range: 379 - 384

DOI: https://doi.org/10.2478/v10006-011-0028-8

Keywords
singular, fractional system, linear circuit, regular pencil, supercapacitor, supercoil

This content is open access.

Singular fractional linear systems and electrical circuits

Published Online: Jun 22, 2011

Page range: 379 - 384

DOI: https://doi.org/10.2478/v10006-011-0028-8

Keywordssingular, fractional system, linear circuit, regular pencil, supercapacitor, supercoil

This content is open access.

Keywords
singular, fractional system, linear circuit, regular pencil, supercapacitor, supercoil