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<p>A fractional-order capacitor (FOC) with order <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(1&lt;\beta &lt;2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>&lt;</mo> <mi>β</mi> <mo>&lt;</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> plays a crucial role in the design of fractional-order circuits. In traditional RLC circuits, incorporating an FOC of this order can enhance the quality factor and reduce the resonance frequency. Despite these advantages, limited research has addressed fractional-order circuits that include nonlinear or non-standard electronic components, such as Zener diodes. To bridge this gap, this paper introduces a novel non-regular fractional RLCD circuit that integrates an FOC with order greater than one. The associated mathematical model is formulated using tools from fractional calculus and monotone operator theory. Finally, numerical simulations are carried out to validate the theoretical analysis and demonstrate the circuit’s behavior.</p>

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A regularization approach to R\(L_{\alpha } C_{\beta }\)D fractional circuit

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Tahar Haddad,
  • Abderrahim Bouach,
  • Ilyas Kecis

摘要

A fractional-order capacitor (FOC) with order \(1<\beta <2\) 1 < β < 2 plays a crucial role in the design of fractional-order circuits. In traditional RLC circuits, incorporating an FOC of this order can enhance the quality factor and reduce the resonance frequency. Despite these advantages, limited research has addressed fractional-order circuits that include nonlinear or non-standard electronic components, such as Zener diodes. To bridge this gap, this paper introduces a novel non-regular fractional RLCD circuit that integrates an FOC with order greater than one. The associated mathematical model is formulated using tools from fractional calculus and monotone operator theory. Finally, numerical simulations are carried out to validate the theoretical analysis and demonstrate the circuit’s behavior.