Electrical circuits RC and RL involving fractional operators with bi-order

Abstract

This article describes electrical series circuits RC and RL using the concept of derivative with two fractional orders α and β in Liouville-Caputo sense. The fractional equations consider derivatives in the range of α, β (0; 1 ]. Numerical solutions are presented considering different source terms introduced in the fractional equation. This new approach considers electrical elements with two different properties. In addition, we prove that if α = 0, the fractional derivative with Mittag-Leffler kernel in Liouville-Caputo sense is recovered, and when β = 0, the Liouville-Caputo fractional derivative is recovered.