v.12 n.5 October

A Variational Problem on the Maximum Energy of a Pulse Generator with a Capacitor Modeled via Conformable Fractional Derivative

Fadime Uyan Kabalar, Reşat Mutlu, and Hafız Alisoy

Parana J. Sci. Educ., v.12, n.5, (1-8),  October 1, 2026.

DOI:  10.5281/zenodo.22698423

Abstract

In this study, a variational problem concerning the maximum energy of a pulse generator with a capacitor modeled via the conformable fractional derivative is solved. The case where the charging circuit of the pulse generator consists of a series-connected R and Cα is examined, and the conformable fractional-order differential equation defining the circuit is provided. For the clarity of the problem, the maximum voltage required to charge the capacitor and the time duration needed for this charging are taken as constant. It is assumed that the capacitor is initially discharged and the capacitor voltage is VC (0) = 0. The equation defining the circuit is transformed into an optimization problem using the Euler-Lagrange equation. Then, this optimization equation is solved using the conformable fractional-order derivative, the finite difference method, and a numerical method for solving boundary value problems. The required numerical solutions were obtained using MATLAB, and the voltage variations of the capacitor modeled with the conformable fractional-order derivative were determined.    

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Erosive Jet Movement (MiniReview)

Vladimir Nikolayevich Sukhanov

Parana J. Sci. Educ., v.12, n.5, (9-14),  October 1, 2026.

DOI: 10.5281/zenodo.21720187

Abstract

A rocket engine of exceptionally simple design, which is easy to manufacture, is described. This is achieved by employing an erosive method to stabilize the combustion of solid propellant within the engine. While the operating principles governing the internal ballistics of such propulsion systems have not previously been formally articulated, the underlying phenomena are known and observed in both nature and technology. The description of the principles of jet propulsion involving external ballistics represents a fundamentally new concept. This explains the jet thrust of meteors moving through the atmosphere, as well as the anomalous acceleration of comets and active asteroids traveling near stars.    

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Measuring Refractive Index Using Raspberry Pi

Rana Demirer, Alpay Doruk, and Reşat Mutlu.

Parana J. Sci. Educ., v.12, n.5, (15-21),  October 1, 2026.

DOI:  10.5281/zenodo.22815914

Abstract

The refractive index is a fundamental optical property characteristic of every substance, serving as a distinct identifier that varies predictably as a function of the operational wavelength of light. In traditional experimental physics, measuring this parameter typically relies on manual optical instruments and mechanical setups, which are often time-consuming, sensitive to environmental disturbances, and prone to user error. To overcome these limitations, this study presents an automated, highly repeatable approach to measuring the refractive index of liquids based on Snell’s law of refraction. By integrating digital image processing methods directly onto a vision-enabled Raspberry Pi microcontroller, the system captures light beam deflection through liquid samples, tracks pixel displacement patterns in real time, and automatically computes the refractive index. This edge-computing setup offers an accurate, cost-effective, and fully automated alternative to conventional laboratory measurements.    

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