Electrical circuits RC, LC, and RL described by Atangana–Baleanu fractional derivatives

Summary In this paper, the analytical solutions for the electrical series circuits RC, LC, and RL using novel fractional derivatives of type Atangana–Baleanu with non‐singular and nonlocal kernel in Liouville–Caputo and Riemann–Liouville sense were obtained. The fractional equations in the time doma...

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Bibliographic Details
Published in:International journal of circuit theory and applications Vol. 45; no. 11; pp. 1514 - 1533
Main Authors: Gómez‐Aguilar, J. F., Atangana, Abdon, Morales‐Delgado, V. F.
Format: Journal Article
Language:English
Published: Bognor Regis Wiley Subscription Services, Inc 01.11.2017
Subjects:
Atangana–Baleanu fractional derivatives
Circuits
Convolution
Derivatives
electrical circuits
fractional differential equations
fractional‐order circuits
Laplace transforms
Mathematical analysis
ISSN:0098-9886, 1097-007X
Online Access:Get full text
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Summary:Summary In this paper, the analytical solutions for the electrical series circuits RC, LC, and RL using novel fractional derivatives of type Atangana–Baleanu with non‐singular and nonlocal kernel in Liouville–Caputo and Riemann–Liouville sense were obtained. The fractional equations in the time domain are considered derivatives in the range α∈(0;1]; analytical solutions are presented considering different source terms introduced in the fractional equation. We solved analytically the fractional equation using the properties of Laplace transform operator together with the convolution theorem. On the basis of the Mittag–Leffler function, new behaviors for the voltage and current were obtained; the classical cases are recovered when α=1. Copyright © 2017 John Wiley & Sons, Ltd. In this paper, we obtain the analytical solutions for the electrical circuits RC, LC, and RL using novel fractional derivatives with non‐singular and non‐local kernel called Atangana–Baleanu fractional derivatives in Liouville–Caputo and Riemann–Liouville sense. The fractional equations in the time domain are considered derivatives in the range αϵ(0;1]; analytical solutions are presented considering different source terms introduced in the fractional equation. We solved analytically the fractional equation using the properties of Laplace transform operator together with the convolution theorem. On the basis of the Mittag–Leffler function, new behaviors for the voltage and current were obtained; the classical cases are recovered when α=1.
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ISSN:0098-9886
1097-007X
DOI:10.1002/cta.2348