v.12 n.2 April

Energy Efficiency of a Resistor-Fractional Order Capacitor Series Circuit During Charging from a DC Voltage Source

Berk Mercan, Alperen Hoçur and Reşat Mutlu.

Parana J. Sci. Educ., v.12, n.2, (1-9),  April 3, 2026.

DOI:  10.5281/zenodo.19153423

Abstract

Fractional-order derivatives offer a significant advantage in modeling complex electrical and electronic systems by providing higher accuracy and flexibility compared to classical integer-order derivative approaches. This method allows for the precise description of the dynamic behavior of energy storing circuit elements, particularly supercapacitors. In recent years, the fractional-order circuit elements have found widespread use in a wide range of applications, from filter designs and control systems to energy storage applications and signal processing. In this study, the energy loss incurred during the charging of a capacitor, modeled using a fractional-order derivative element in series with a resistor and driven by a DC source, is analytically examined. The analysis is conducted using the Caputo definition of the fractional derivative. The results are then compared with the energy loss in a classical R–C circuit. The findings indicate that the energy loss in a fractional-order capacitor-resistor circuit during charging differs from that in an integer-order counterpart. It is found to be dependent on the fractional order α. .Fractional-order modeling of the capacitor is needed to calculate the charging efficiency of such a circuit accurately.

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Numerical Analysis of a Liénard Oscillator with Fractional Order Circuit Elements

İrem Batibey, Nisanur Durukan and Reşat Mutlu.

Parana J. Sci. Educ., v.12, n.2, (10-23),  April 3, 2026.

DOI:  10.5281/zenodo.19153469

Abstract

The Liénard oscillator is a nonlinear dynamical system governed by a differential equation that incorporates both damping and restoring terms. It is widely used in physics and engineering to model self-sustained oscillations, including electrical circuits and biological rhythms. A special case of this oscillator is the Van der Pol oscillator, which exhibits limit cycles and nonlinear behavior. The Liénard oscillator plays a crucial role in understanding complex oscillatory phenomena in both classical and quantum mechanics. In the last half century, fractional-order circuit elements have become very popular. They can be used to model electrical components, circuits, systems, etc. A Liénard oscillator can also be modified to have a fractional-order capacitor and a fractional-order inductor instead of the LTI ones. In this case, the oscillator is still nonlinear, and a numerical method should be used to solve it. Fractional-order derivatives introduce more design parameters that allow designing a more flexible Liénard oscillator with more complex dynamical behavior than one with classical integer-order derivatives or the LTI circuit elements. This article models the use of a fractional-order capacitor and a fractional-order inductor in a Liénard oscillator and examines its dynamical behavior parametrically using the Grünwald-Letnikov Fractional derivative. The performance of fractional- order circuit elements in the Liénard oscillator is evaluated considering their parameters. The results show that usage of the fractional order circuit elements results in a more complex behavior of Liénard oscillators due to having extra parameters.

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The Architecture of Exuberance: Planning for Excess in Scarcity

Soumyadeep Dutta, and Abhijit Basak.

Parana J. Sci. Educ., v.12, n.2, (24-31),  April 3, 2026.

DOI:  10.5281/zenodo.19153518

Abstract

In the architectural history of post-independence India, few interventions have generated as much polarized discourse as the Dr. Bhimrao Ambedkar Samajik Parivartan Prateek Sthal (Dr. B.R. Ambedkar Social Change Memorial) in Lucknow. Situated in the sprawling Gomti Nagar district, this 108-acre complex stands as the apotheosis of a specific political and aesthetic vision commissioned by the Bahujan Samaj Party (BSP). It represents a deliberate rupture from Lucknow's existing urban fabric—defined by Nawabi brickwork and colonial neo-classicism—to establish a permanent "Dalit presence" via massive stone interventions. The analysis confirms that the park's planning prioritizes the "gaze" over "use," resulting in a space that is thermally dangerous and socially exclusionary during the day. The path forward lies in Adaptive Reuse: treating the park not as a finished static monument, but as a base infrastructure that must be retrofitted with shade, greenery, and social programs. By converting "hard" waste into "soft" assets, the site can evolve from a stone curtain into a living, breathing civic space.

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