Analytical solutions of electrical circuits described by fractional conformable derivatives in Liouville-Caputo sense

In this paper, new analytical solutions for the RL, LC and RLC electric circuits considering conformable and β-derivatives of type Liouville-Caputo were analyzed. These solutions were obtained by iterating conformable and β-integrals. The fractional derivatives considered have properties similar to...

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Vydáno v:International journal of electronics and communications Ročník 85; s. 108 - 117
Hlavní autoři: Morales-Delgado, V.F., Gómez-Aguilar, J.F., Taneco-Hernandez, M.A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier GmbH 01.02.2018
Témata:
Conformable-derivative
Electrical circuits
Exact analytical solutions
Liouville-Caputo derivative
Riemann-Liouville derivative
β-derivative
Exact analytical solutions
Riemann-Liouville derivative
Conformable-derivative
Electrical circuits
β-derivative
Liouville-Caputo derivative
ISSN:1434-8411, 1618-0399
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Shrnutí:In this paper, new analytical solutions for the RL, LC and RLC electric circuits considering conformable and β-derivatives of type Liouville-Caputo were analyzed. These solutions were obtained by iterating conformable and β-integrals. The fractional derivatives considered have properties similar to the classical fractional integrals and derivatives. Due to these operators depend on two parameters, we obtain a better detection of the memory. Novel fractional conformable β-derivatives in the Riemann-Liouville and the Liouville-Caputo sense are obtained. Numerical simulations of alternative models are presented for evaluating the effectiveness of these representations. Different source terms are introduced in the fractional conformable differential equations in Liouville-Caputo sense.
ISSN:1434-8411
1618-0399
DOI:10.1016/j.aeue.2017.12.031