Analytical and numerical solutions of electrical circuits described by fractional derivatives

•Developed new fractional models of electrical circuits RC, RL, RLC, power electronic devices and nonlinear loads.•Obtained analytical and numerical solutions of fractional models.•To keep the dimensionality an auxiliary parameter σ is introduced. This paper deals with the application of fractional...

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Bibliographic Details
Published in:Applied mathematical modelling Vol. 40; no. 21-22; pp. 9079 - 9094
Main Authors: Gómez-Aguilar, J.F., Yépez-Martínez, H., Escobar-Jiménez, R.F., Astorga-Zaragoza, C.M., Reyes-Reyes, J.
Format: Journal Article
Language:English
Published: Elsevier Inc 01.11.2016
Subjects:
Caputo–Fabrizio fractional derivative
Electrical circuits
Fractional calculus
Liouville–Caputo fractional derivative
Mittag–Leffler function
Riemann–Liouville fractional derivative
33E12
Liouville–Caputo fractional derivative
Riemann–Liouville fractional derivative
44A10
94C05
26A33
Caputo–Fabrizio fractional derivative
Mittag–Leffler function
Fractional calculus
Electrical circuits
ISSN:0307-904X
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Summary:•Developed new fractional models of electrical circuits RC, RL, RLC, power electronic devices and nonlinear loads.•Obtained analytical and numerical solutions of fractional models.•To keep the dimensionality an auxiliary parameter σ is introduced. This paper deals with the application of fractional derivatives in the modeling of electrical circuits RC, RL, RLC, power electronic devices and nonlinear loads, the equations are obtained by replacing the time derivative by fractional derivatives of type Riemann–Liouville, Grünwald–Letnikov, Liouville–Caputo and the fractional definition recently introduced by Caputo and Fabrizio. The fractional equations in the time domain considers derivatives in the range of α ∈ (0; 1], analytical and numerical results are presented considering different source terms introduced in the fractional equation. The resulting solutions modified the capacitance, inductance, also, the resistance exhibits fluctuations or fractality of time in different scales. Furthermore, the results showed the existence of heterogeneities in the electrical components causing irreversible dissipative effects. The classical models are recovered when the order of the fractional derivatives are equal to 1.
ISSN:0307-904X
DOI:10.1016/j.apm.2016.05.041