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Electrical circuits RC, LC, and RL described by Atangana–Baleanu fractional derivatives
Author(s) -
GómezAguilar J. F.,
Atangana Abdon,
MoralesDelgado V. F.
Publication year - 2017
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.2348
Subject(s) - laplace transform , fractional calculus , mathematics , convolution (computer science) , type (biology) , kernel (algebra) , mathematical analysis , operator (biology) , mittag leffler function , function (biology) , pure mathematics , computer science , artificial neural network , ecology , biochemistry , chemistry , repressor , machine learning , transcription factor , gene , biology , evolutionary biology
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.