Research Article

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

Volume: 12 Number: 1 April 30, 2024
EN

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

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.

Keywords

References

  1. [1] H. Akc¸a, J. Benbourenane H. Eleuch, The q -derivative and differential equation, J. Phys. Conf. Ser., (2019), 1411:012002.
  2. [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. [3] S. Y. Arbab and S. H. Altoum, q-Bernoulli’s Equation, Am. J. Appl. Sci., 17(1)(2020), 214-217.
  4. [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. [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. [6] H. Cheng, Canonical Quantization of Yang-Mills Theories, Perspectives in Mathematical Physics, International Press, Somerville, MA, USA, 1996.
  7. [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. [8] A. Ebaid, B. Masaedeh, E. El-Zahar, A new fractional model for the falling body problem, Chin. Phys. Lett., 34(2)(2017), 020201.

Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Early Pub Date

April 29, 2024

Publication Date

April 30, 2024

Submission Date

June 7, 2023

Acceptance Date

January 26, 2024

Published in Issue

Year 2024 Volume: 12 Number: 1

APA
Turan, N., & Basarır, M. (2024). On the Solutions of Some Equations in $(p,q)$-Calculus. Konuralp Journal of Mathematics, 12(1), 21-27. https://izlik.org/JA92CY64AN
AMA
1.Turan N, Basarır M. On the Solutions of Some Equations in $(p,q)$-Calculus. Konuralp J. Math. 2024;12(1):21-27. https://izlik.org/JA92CY64AN
Chicago
Turan, Nihan, and Metin Basarır. 2024. “On the Solutions of Some Equations in $(p,q)$-Calculus”. Konuralp Journal of Mathematics 12 (1): 21-27. https://izlik.org/JA92CY64AN.
EndNote
Turan N, Basarır M (April 1, 2024) On the Solutions of Some Equations in $(p,q)$-Calculus. Konuralp Journal of Mathematics 12 1 21–27.
IEEE
[1]N. Turan and M. Basarır, “On the Solutions of Some Equations in $(p,q)$-Calculus”, Konuralp J. Math., vol. 12, no. 1, pp. 21–27, Apr. 2024, [Online]. Available: https://izlik.org/JA92CY64AN
ISNAD
Turan, Nihan - Basarır, Metin. “On the Solutions of Some Equations in $(p,q)$-Calculus”. Konuralp Journal of Mathematics 12/1 (April 1, 2024): 21-27. https://izlik.org/JA92CY64AN.
JAMA
1.Turan N, Basarır M. On the Solutions of Some Equations in $(p,q)$-Calculus. Konuralp J. Math. 2024;12:21–27.
MLA
Turan, Nihan, and Metin Basarır. “On the Solutions of Some Equations in $(p,q)$-Calculus”. Konuralp Journal of Mathematics, vol. 12, no. 1, Apr. 2024, pp. 21-27, https://izlik.org/JA92CY64AN.
Vancouver
1.Nihan Turan, Metin Basarır. On the Solutions of Some Equations in $(p,q)$-Calculus. Konuralp J. Math. [Internet]. 2024 Apr. 1;12(1):21-7. Available from: https://izlik.org/JA92CY64AN
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.