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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 74 Issue: 2

On special ruled surface pairs in fractional calculus

Zehra Nur Koçak(ANKARA HACI BAYRAM VELI UNIVERSITY)0009-0001-1631-2063
Emel Karaca(Ankara Hacı Bayram Veli Üniversitesi)0000-0003-0703-939X
Pages
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Publication Date
2025-06-19
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we give examples to verify the results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we extend the theory of special fractional curve pairs (i.e., F-Bertrand, FMannheim, and F-involute-evolute curve pairs) to fractional ruled surfaces with the perspective of fractional calculus.
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Key Findings & Data:Moreover, considering the chain rules in fractional calculus, some significant theorems are proved, and the developability conditions are examined by calculating the distribution parameters.
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Conclusion & Impact:Finally, we give examples to verify the results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fractional derivative and integrals · ruled surface · special surfaces

Abstract

In this paper, we extend the theory of special fractional curve pairs (i.e., F-Bertrand, FMannheim, and F-involute-evolute curve pairs) to fractional ruled surfaces with the perspective of fractional calculus. Next, we characterize two fractional ruled surfaces, offset in the senses of F-Bertrand, F-Mannheim, and F-involute-evolute. Moreover, considering the chain rules in fractional calculus, some significant theorems are proved, and the developability conditions are examined by calculating the distribution parameters. Finally, we give examples to verify the results.

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Cite This Article

Koçak, Z. N., Karaca, E. (2025). On special ruled surface pairs in fractional calculus. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 74 Issue: 2. https://doi.org/10.31801/cfsuasmas.1500845

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