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.
Summary
In this paper, we study a supercapacitor model represented by an equivalent RC circuit considering five different types of derivatives: Caputo, Caputo‐Fabrizio, and Atangana‐Baleanu fractional derivatives and the conformable and integer‐order derivatives. A set of experimental data from six commercial supercapacitors are used to estimate the parameter values for each derivative model by applying interior point optimization. The results show that the most accurate approach is achieved with the conformable derivative followed by the Caputo fractional derivative.
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