SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 71 Issue: 3

On the solutions of the q-analogue of the telegraph differential equation

Döne Karahan(HARRAN ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ)0000-0001-6644-5596
Pages
—
Publication Date
2022-09-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

The results showed that the method is useful and effective for q-analogue of the telegraph differential equation.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, q-analogue of the telegraph differential equation is investigated.
📊
Key Findings & Data:The approximation solution of q-analogue of the telegraph differential equation is founded by using the Laplace transform collocation method (LTCM).
💡
Conclusion & Impact:The results showed that the method is useful and effective for q-analogue of the telegraph differential equation.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:q-analogue of the telegraph differential equation · Laplace transform collocation method · exact solution

Abstract

In this work, q-analogue of the telegraph differential equation is investigated. The approximation solution of q-analogue of the telegraph differential equation is founded by using the Laplace transform collocation method (LTCM). Then, the exact solution is compared with the approximation solution for q-analogue of the telegraph differential equation. The results showed that the method is useful and effective for q-analogue of the telegraph differential equation.

🔖

Cite This Article

Karahan, D. (2022). On the solutions of the q-analogue of the telegraph differential equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 71 Issue: 3. https://doi.org/10.31801/cfsuasmas.1009068

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (13)

  1. Euler, L., Introduction in Analysin Infinitorum, vol. 1, Lausanne, Switzerland, Bousquet, 1748.
  2. Ernst, T., The History of q-Calculus and a New Method, U.U.D.M. Report 2000, 16, Uppsala, Department of Mathematics, Uppsala University, 2000.
  3. Kac, V., Cheung, P., Quantum Calculus, Universitext, Springer, New York, 2002.
  4. Annaby, M.H., Mansour, Z.S., q-Fractional Calculus and Equations, Lecture Notes in Mathematics, vol. 2056, Springer, Heidelberg, 2012. https://doi.org/10.1007/978-3-642- 30898-7
  5. Karahan, D., Mamedov, Kh.R., Sampling theory associated with q-Sturm-Liouville operator with discontinuity conditions, Journal of Contemporary Applied Mathematics, 10(2) (2020), 1-9.
  6. Liu, Z.G., On a System of q-Partial Differential Equations with Applications to q-Series, In:Andrews G., Garvan F., Analytic Number Theory, Modular Forms and q-Hypergeometric Series, ALLADI60 2016, Springer Proceedings in Mathematics and Statistics, Vol. 221, Springer, 2017.
  7. Liu, Z.G., On the q-Partial Differential Equations and q-Series. In: The Legacy of Srinivasa Ramanujan, 213-250, Ramanujan Mathematical Society Lecture Notes Series, Vol. 20, Ramanujan Mathematical Society, Mysore, 2013.
  8. Cao, J., Homogeneous q-partial difference equations and some applications, Advances in Applied Mathematics, 84 (2017), 47-72. https://doi.org/10.1016/j.aam.2016.11.001
  9. Adewumi, A.O., Akindeinde, S.O., Aderogba, A.A., Ogundare, B.S., Laplace transform collocation method for solving hyperbolic telegraph equation, International Journal of Engineering Mathematics, (2017). https://doi.org/10.1155/2017/3504962
  10. Modanli, M., Laplace transform collocation and Daftar-Gejii-Jafaris method for fractional order time varying linear dynamical systems, Physica Scripta, 96(9) (2021), 094003. https://doi.org/10.1088/1402-4896/ac00e7
  11. Hahn, W., Beitrage zur Theorie der Heineschen Reihen (German), Math. Nachr., 2 (1949), 340-379. https://doi.org/10.1002/mana.19490020604
  12. Daiz, R., Ternel C., q, k-generalized gamma and beta functions, J. Nonlinear Math. Phys., 12(1) (2005), 118-131.
  13. De Sole, A., Kac, V.G., On integral representations of q-gamma and q-beta functions, Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, 16(1) (2005), 11-29.