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Dergiler / Konuralp Journal of Mathematics / 2026 / Volume: 12 Issue: 1

On the Solutions of Some Equations in $(p,q)$-Calculus

Nihan Turan(SAKARYA ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ, MATEMATİK (DR))
Metin Basarır(SAKARYA ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ)0000-0002-4341-4399
Sayfa
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Yayın Tarihi
2024-04-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, we obtain the solution of the Bernoulli’s equation in $(p,q)$-calculus.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we introduce the Laplace equation in $(p, q)$-calculus and give the solutions of the equation using the separation method into its variables.
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Temel Bulgular & Veri:We also give the $(p,q)$-calculus version of the equation of motion, which expresses the displacement of a falling field in a resistant environment.
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Sonuç & Katkı:Finally, we obtain the solution of the Bernoulli’s equation in $(p,q)$-calculus.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Falling Field Problem · Laplace Equation · Bernoulli

Abstract

In this paper, we introduce the Laplace equation in $(p, q)$-calculus and give the solutions of the equation using the separation method into its variables. We also give the $(p,q)$-calculus version of the equation of motion, which expresses the displacement of a falling field in a resistant environment. Finally, we obtain the solution of the Bernoulli’s equation in $(p,q)$-calculus.

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Bu Makaleye Atıf Yap

Turan, N., Basarır, M. (2024). On the Solutions of Some Equations in $(p,q)$-Calculus. Konuralp Journal of Mathematics, Volume: 12 Issue: 1. https://ajindex.com/articles/1521500

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Kaynakça (24)

  1. H. Akc¸a, J. Benbourenane H. Eleuch, The q -derivative and differential equation, J. Phys. Conf. Ser., (2019), 1411:012002.
  2. A. M. Alanazi, A. Ebaid, W. M. Alhawiti and G. Muhiuddin, The falling body problem in quantum calculus, Front. Phys., 8(43)(2020).
  3. S. Y. Arbab and S. H. Altoum, q-Bernoulli’s Equation, Am. J. Appl. Sci., 17(1)(2020), 214-217.
  4. N. Bettaibi and K. Mezlini, On the use Of the q-Mellin transform to solve some q-heat and q-wave equations, Int. J. Math. Arch., 3(2)(2012), 446-455.
  5. R. Chakrabarti and R. Jagannathan, A (p;q)-oscillator realization of two parameter quantum algebras, J. Phys. A: Math. Gen., 24(13)(1991), 5683-5701.
  6. H. Cheng, Canonical Quantization of Yang-Mills Theories, Perspectives in Mathematical Physics, International Press, Somerville, MA, USA, 1996.
  7. U. Duran, S. Aracı, and M. Ac¸ıkg¨oz, A Study on Some New Results Arising from (p;q)-Calculus, TWMS J. Pure Appl. Math., 11(1)(2020), 57-71.
  8. A. Ebaid, B. Masaedeh, E. El-Zahar, A new fractional model for the falling body problem, Chin. Phys. Lett., 34(2)(2017), 020201.
  9. R. Floreanini and L. Vinet, q-gamma and q-beta functions in quantum algebra representation theory, J. Comput. Appl. Math., 68(1-2)(1996), 57–68.
  10. J.J.R. Garcia, M.G. Calderon, J.M. Ortiz, D. Baleanu, Motion of a particle in a resisting medium using fractional calculus approach, Proc. Roman Acad Ser A., 14(1)(2013), 42-47.
  11. ˙I. Genc¸t¨urk, Boundary value problems for a second-order (p;q)-difference equation with integral conditions, Turk. J. Math., 46(2)(2022), 499-515.
  12. G.H. Hardy and E.M.Wright, An Introduction to the Theory of Numbers, Oxford University Press, 1960.
  13. F.H. Jackson, q-Diference Equations, American J. Math., 32(4)(1910), 305-314.
  14. R. Jagannathan, and K.S. Rao, Two-parameter quantum algebras, twin basic numbers and associated generalized hypergeometric series, In Proceeding of the International Conference on Number Theory and Mathematical Physics, Srinivasa Ramanujan Centre, Kumbakonam, India (2005).
  15. V. Kac and C. Pokman, Quantum Calculus, Springer, 2002.
  16. N. Kamsrisuk, C. Promsakon, S.K. Ntouyas, J. Tariboon, Nonlocal boundary value problems for (p;q)-difference equations, Differ. Equ. Appl., 10(2)(2018), 183-195.
  17. G. Kaniadakis, A. Lavagno, and P. Quarati, Kinetic model for q-deformed bosons and fermions, Phys. Lett. A, 227(3)(1997), 227-231.
  18. G.V. Milovanovic, V. Gupta, N. Malik, (p;q)-Beta functions and applications in approximation, Bol. Soc. Mat. Mex., 24(1)(2018), 219-237.
  19. M. Mursaleen, M. Nasiruzzaman, A. Khan, K.J. Ansari, Some approximation results on Bleimann Butzer Hahn operators defined by (p;q)-integers, Filomat, 30(3)(2016), 639-648.
  20. P.N. Sadjang, On the fundamental theorem of (p;q)-calculus and some (p;q)-Taylor formulas, Result. Math., 73(1)(2018), 1-21.
  21. W. J. Trjitzinsky, Analytic theory of linear q-difference equations, Act. Math., 62(1)(1933), 167–226.
  22. N. Turan and M. Bas¸arır, The Solutions of Motion, Laplace And Bernoulli’s Equations in q-Calculus, 9th Internatıonal Zeugma Conference On Scıentıfıc Research, February 19-21, 2023 / Gaziantep, T¨urkiye, full text book, page 144-151, ISBN:978-625-6404-76-2.
  23. J.J.R. Garcia, M.G. Calderon, J.M. Ortiz, D. Baleanu, Motion of a particle in a resisting medium using fractional calculus approach, Proc. Roman Acad Ser A., 14(1)(2013), 42-47.
  24. ˙I. Genc¸t¨urk, Boundary value problems for a second-order (p;q)-difference equation with integral conditions, Turk. J. Math., 46(2)(2022), 499-515.