Fractional Operators for Nonlinear Electrical Circuits

TL;DR

This paper introduces two novel fractional operators with sine and cosine kernels, aimed at simplifying the analysis of nonlinear electrical circuits with memory effects, especially for components like memristors.

Contribution

The paper presents new fractional operators with sine and cosine kernels that facilitate the analysis of nonlinear electrical systems with memory effects, a novel approach in this field.

Findings

Operators enable linearization of nonlinear equations in electrical circuits.

Application to memristor models shows improved analytical tractability.

Potential for enhanced modeling of AC signals in complex circuits.

Abstract

This article introduces two new fractional operators with sine ($\sin$) and cosine ($\cos$) kernels, motivated by their fundamental role in modeling AC signals in electrical circuits. The operators are designed to improve the analysis of nonlinear components such as the memristor by transforming certain nonlinear equations into simpler linear forms, particularly in systems with memory effects.