A New Look at the Capacitor Theory
Manuel Duarte Ortigueira, Valeriy Martynyuk, Volodymyr Kosenkov, Arnaldo Batista
Abstract
The mathematical description of the charging process of time-varying capacitors is reviewed and a new formulation is proposed. For it, suitable fractional derivatives are described. The case of fractional capacitors that follow the Curie–von Schweidler law is considered. Through suitable substitutions, a similar scheme for fractional inductors is obtained. Formulae for voltage/current input/output are presented. Backward coherence with classic results is established and generalised to the variable order case. The concept of a tempered fractor is introduced and related to the Davidson–Cole model.
Topics & Concepts
CapacitorInductorVoltageCoherence (philosophical gambling strategy)Fractional calculusMathematicsProcess (computing)Scheme (mathematics)Current (fluid)CurieControl theory (sociology)Topology (electrical circuits)Computer scienceApplied mathematicsPhysicsMathematical analysisElectrical engineeringCurie temperatureEngineeringQuantum mechanicsFerromagnetismCombinatoricsOperating systemStatisticsArtificial intelligenceControl (management)Advanced Control Systems DesignFractional Differential Equations SolutionsChaos control and synchronization