Investigating the dynamics of Hilfer fractional operator associated with certain electric circuit models.

Summary: The present manuscript investigates the action of the Hilfer fractional operator on the dynamics of resistor–capacitor (RC) and certain resistor–inductor‐capacitor (RLC) electric circuits using the Laplace transform method alongside utilizing the negative binomial formula. The choice of Hilfer's operator here was basically based on its interpolating nature between the well‐known Caputo and Riemann–Liouville fractional derivatives. Meanwhile, this operator has not been adequately scrutinized with regard to its effects on electric circuits in the literature. Thus, respective approximate exact solutions are determined convolutionally in the presence of certain periodic voltage source functions. Lastly, the significance of the operator on the dynamics of these models was demonstrated graphically for different values of the fractional‐order α and type β. More so, the present study will be beneficial in designing modern electric devices involving temporal delays and memory record. [ABSTRACT FROM AUTHOR]