Fractional calculus approach to a single loop RL circuit
This paper derived the solutions for the current growth and current decay of a single loop RL circuit in Caputo and Riemann–Liouville formulations. The plots of the current decay and current growth in fractional formulations are compared to the current decay and current growth in ordinary differential equation (ODE) with the tolerance being accounted. This paper investigates which fractional order has the least deviation to the ODE solutions when the maximum tolerance of 5% of the resistor is applied. The authors used independent paired t-test to assess the significant difference between the fractional order formulations and the ODE solutions. Ten samples are taken from fractional formulations and ODE solution. A confidence level of 95% and two-tailed analysis was used in this paper. A notable phenomenon in the fractional formulations plot that the authors named as current inverse time is briefly discussed.