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Numerical Solution of Conformable Time Fractional Generalized Burgers Equation with Proportional Delay by New Methods

Cilt: 13 Sayı: 2 15 Haziran 2023
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Numerical Solution of Conformable Time Fractional Generalized Burgers Equation with Proportional Delay by New Methods

Öz

By using two new methods, called the conformable fractional q-homotopy analysis transform method and the conformable Shehu homotopy perturbation method, the conformable time-fractional partial differential equations with proportional delay is analysed. The graphs of this equation's numerical solutions are drawn. According to numerical simulations, the proposed methods are effective and reliable.

Anahtar Kelimeler

Conformable time fractional generalized Burgers equation, conformable q-homotopy analysis transform method, conformable Shehu homotopy perturbation method, proportional delay

Kaynakça

  1. Abazari, R., and Ganji, M. (2011). Extended two-dimensional DTM and its application on nonlinear PDEs with proportional delay. International Journal of Computer Mathematics, 88(8), 1749–1762.
  2. Abazari, R., and Kılıcman, A. (2014). Application of differential transform method on nonlinear integro–differential equations with proportional delay. Neural Computing and Applications, 24(2), 391–397.
  3. Abdeljawad, T. (2015). On conformable fractional calculus. Journal of Computational and Applied Mathematics, 279, 57-66.
  4. Ala, V. (2022). New exact solutions of space-time fractional Schrödinger-Hirota equation. Bulletin of the Karaganda University Mathematics Series, 107(3).
  5. Ala, V., and Shaikhova, G. (2022). Analytical Solutions of Nonlinear Beta Fractional Schrödinger Equation Via Sine-Cosine Method. Lobachevskii Journal of Mathematics, 43(11), 3033-3038.
  6. Alkan, A. (2022). Improving homotopy analysis method with an optimal parameter for time-fractional Burgers equation. Karamanoğlu Mehmetbey Üniversitesi Mühendislik ve Doğa Bilimleri Dergisi, 4(2), 117-134.
  7. Baleanu, D., Diethelm, K., Scalas, E., and Trujillo, J. J., (2012). Fractional Calculus: Models and Numerical Methods. Boston, USA: World Scientific.
  8. Baleanu, D., Wu, G. C., and Zeng, S. D., (2017). Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations. Chaos Solitons Fractals, 102, 99–105.
  9. Benattia, M. E., and Belghaba, K. (2021). Shehu conformable fractional transform, theories and applications. Cankaya University Journal of Science and Engineering, 18(1), 24-32.
  10. Biazar, J., and Ghanbari, B. (2012). The homotopy perturbation method for solving neutral functional-differential equations with proportional delays. Journal of King Saud University-Science, 24 (1), 33–37.

Kaynak Göster

APA
Kartal, A., Anaç, H., & Olgun, A. (2023). Numerical Solution of Conformable Time Fractional Generalized Burgers Equation with Proportional Delay by New Methods. Karadeniz Fen Bilimleri Dergisi, 13(2), 310-335. https://doi.org/10.31466/kfbd.1191870
AMA
1.Kartal A, Anaç H, Olgun A. Numerical Solution of Conformable Time Fractional Generalized Burgers Equation with Proportional Delay by New Methods. KFBD. 2023;13(2):310-335. doi:10.31466/kfbd.1191870
Chicago
Kartal, Abdullah, Halil Anaç, ve Ali Olgun. 2023. “Numerical Solution of Conformable Time Fractional Generalized Burgers Equation with Proportional Delay by New Methods”. Karadeniz Fen Bilimleri Dergisi 13 (2): 310-35. https://doi.org/10.31466/kfbd.1191870.
EndNote
Kartal A, Anaç H, Olgun A (01 Haziran 2023) Numerical Solution of Conformable Time Fractional Generalized Burgers Equation with Proportional Delay by New Methods. Karadeniz Fen Bilimleri Dergisi 13 2 310–335.
IEEE
[1]A. Kartal, H. Anaç, ve A. Olgun, “Numerical Solution of Conformable Time Fractional Generalized Burgers Equation with Proportional Delay by New Methods”, KFBD, c. 13, sy 2, ss. 310–335, Haz. 2023, doi: 10.31466/kfbd.1191870.
ISNAD
Kartal, Abdullah - Anaç, Halil - Olgun, Ali. “Numerical Solution of Conformable Time Fractional Generalized Burgers Equation with Proportional Delay by New Methods”. Karadeniz Fen Bilimleri Dergisi 13/2 (01 Haziran 2023): 310-335. https://doi.org/10.31466/kfbd.1191870.
JAMA
1.Kartal A, Anaç H, Olgun A. Numerical Solution of Conformable Time Fractional Generalized Burgers Equation with Proportional Delay by New Methods. KFBD. 2023;13:310–335.
MLA
Kartal, Abdullah, vd. “Numerical Solution of Conformable Time Fractional Generalized Burgers Equation with Proportional Delay by New Methods”. Karadeniz Fen Bilimleri Dergisi, c. 13, sy 2, Haziran 2023, ss. 310-35, doi:10.31466/kfbd.1191870.
Vancouver
1.Abdullah Kartal, Halil Anaç, Ali Olgun. Numerical Solution of Conformable Time Fractional Generalized Burgers Equation with Proportional Delay by New Methods. KFBD. 01 Haziran 2023;13(2):310-35. doi:10.31466/kfbd.1191870