Fractional input stability for electrical circuits described by the Riemann-Liouville and the Caputo fractional derivatives

Ndolane Sene; Ndolane Sene

doi:10.3934/Math.2019.1.147

AIMS Mathematics

2019, Volume 4, Issue 1: 147-165. doi: 10.3934/Math.2019.1.147

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Fractional input stability for electrical circuits described by the Riemann-Liouville and the Caputo fractional derivatives

Ndolane Sene ^,

Laboratoire Lmdan, Département de Mathématiques de la Décision, Université Cheikh Anta Diop de Dakar, Faculté des Sciences Economiques et Gestion, BP 5683 Dakar Fann, Senegal

Received: 13 December 2018 Accepted: 27 January 2019 Published: 15 February 2019

The fractional input stability of the electrical circuit equations described by the fractional derivative operators has been investigated. The Riemann-Liouville and the Caputo fractional derivative operators have been used. The analytical solutions of the electrical circuit equations have been developed. The Laplace transforms of the Riemann-Liouville, and the Caputo fractional derivative operators have been used. The graphical representations of the analytical solutions of the electrical circuit equations have been presented. The converging-input converging-state property of the electrical RL, RC and LC circuit equations described by the Caputo fractional derivative, and the global asymptotic stability property of the unforced electrical circuit equations have been illustrated.
- fractional derivatives,
- electrical circuits,
- fractional differential equations
Citation: Ndolane Sene. Fractional input stability for electrical circuits described by the Riemann-Liouville and the Caputo fractional derivatives[J]. AIMS Mathematics, 2019, 4(1): 147-165. doi: 10.3934/Math.2019.1.147

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Abstract

The fractional input stability of the electrical circuit equations described by the fractional derivative operators has been investigated. The Riemann-Liouville and the Caputo fractional derivative operators have been used. The analytical solutions of the electrical circuit equations have been developed. The Laplace transforms of the Riemann-Liouville, and the Caputo fractional derivative operators have been used. The graphical representations of the analytical solutions of the electrical circuit equations have been presented. The converging-input converging-state property of the electrical RL, RC and LC circuit equations described by the Caputo fractional derivative, and the global asymptotic stability property of the unforced electrical circuit equations have been illustrated.

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