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Electrical circuits described by fractional conformable derivative
Author(s) -
Martínez L.,
Rosales J.J.,
Carreño C.A.,
Lozano J.M.
Publication year - 2018
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.2475
Subject(s) - fractional calculus , derivative (finance) , mathematics , rlc circuit , capacitance , lcr meter , inductance , rc circuit , mathematical analysis , electronic circuit , generalizations of the derivative , physics , capacitor , voltage , quantum mechanics , electrode , financial economics , economics
Summary In the last 3 years, the fractional conformable derivative and its properties have been introduced. Unlike other definitions, this new fractional derivative is based on the basic limit definition of the derivative and satisfies the same formulas of derivation, such as product and quotient of 2 functions and the chain rule. Using this new derivative, we obtain a new class of linear ordinary differential equations with noninteger power variable coefficients for the Resistance Capacitance (RC), Inductance Capacitance (LC), and Resistance, Inductance Capacitance (RLC) electric circuits. The numerical solutions are solved through the Matlab software. Solutions depend on time and on the fractional order parameter 0 < γ ≤ 1. The computing using this new derivative is much easier than using other definitions of fractional derivative. It has been shown that in the particular case γ = 1, these solutions become the ordinary ones. Also, a comparison has been made with the Caputo fractional derivative for the case of the RC circuit with constant source.