Journal
INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS
Volume 45, Issue 11, Pages 1514-1533Publisher
WILEY
DOI: 10.1002/cta.2348
Keywords
electrical circuits; fractional differential equations; Atangana-Baleanu fractional derivatives; fractional-order circuits
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Funding
- CONACyT: catedras CONACyT para jovenes investigadores
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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 (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 =1. Copyright (c) 2017 John Wiley & Sons, Ltd.
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