Yıl: 2021 Cilt: 21 Sayı: 2 Sayfa Aralığı: 496 - 506 Metin Dili: İngilizce DOI: 10.35414/akufemubid.860771 İndeks Tarihi: 22-11-2021

Constructions Of Traveling Wave Solutions Of The Fractional NonlinearModel Of The Low-Pass Electrical Transmission Lines

Öz:
In this article, the structure of the improved 𝑡𝑎𝑛(𝜑/2)-expansion method and the simplest equation method are applied. The fractional nonlinear model of the low-pass electrical transmission lines via Atangana-Baleanu derivative operator is taken into consideration and exact solutions have been constructed of this equation using proposed methods. This article explores the applicability and effectiveness of these methods on fractional nonlinear evolution equations.
Anahtar Kelime:

Alçak Geçiren Elektrik İletim Hatlarının Kesirli Mertebeden Lineer Olmayan Modelinin İlerleyen Dalga Çözümlerinin Oluşturulması

Öz:
Bu makalede, geliştirilmiş 𝑡𝑎𝑛(𝜑/2)-açılım yöntemi ve en basit denklem yöntemi uygulanmıştır. Alçakgeçiren elektrik iletim hatlarının Atangana-Baleanu türev operatörü aracılığıyla kesirli mertebedenlineer olmayan modeli dikkate alınmış ve önerilen yöntemler kullanılarak bu denklemin tam çözümlerioluşturulmuştur. Bu makale, bu yöntemlerin kesirli doğrusal olmayan evrim denklemleri üzerindekiuygulanabilirliğini ve etkinliğini araştırmaktadır.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
1
1
1
  • Abdoulkary, S., Beda, T., Dafounamssou, O., Tafo, E. W., Mohamadou, A., 2013. Dynamics of solitary pulses in the nonlinear low-pass electrical transmission lines through the auxiliary equation method. J. Mod. Phys. Appl., 2, 69-87.
  • Abdou, M.A. and Soliman, A.A., 2018. New exact travelling wave solutions for space-time fractional nonlinear equations describing nonlinear transmission lines. Results in Physics, 9, 1497-1501.
  • Alderremy, A. A., Attia, R. A., Alzaidi, J. F., Lu, D., Khater, M., 2019. Analytical and semi-analytical wave solutions for longitudinal wave equation via modified auxiliary equation method and Adomian decomposition method. Thermal Science, 00, 355- 355.
  • Atangana, A., Baleanu, D., 2016. New fractional derivatives with nonlocal and nonsingular kernel: Theory and application to heat transfer model. Thermal Science, 20, 2, 763- 769.
  • Atangana, A., Gomez-Aguilar, J.F. , 2018. Numerical approximation of Riemann-Liouville definition of fractional derivative: from Riemann-Liouville to Atangana-Baleanu. Numerical Methods for Partial Differential Equations, 34, 5, 1502-1523.
  • Atangana, A. And Koca, İ., 2016. Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order. Chaos Solitons Fractals 89, 447-454.
  • Caputo, M. , 1967. Linear models of dissipation whose q is almost frequency independentâ ’ ii. Geophysical Journal International, 13, 5, 529-539.
  • Caputo, M. and Fabrizio, M., 2015. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications, 1, 2,1-13.
  • Durur, H., 2020. Different types analytic solutions of the (1+ 1)-dimensional resonant nonlinear Schrödinger’s equation using (G′/G)-expansion method. Modern Physics Letters B, 34, 03, 2050036.
  • Durur, H., Yokuş, A., 2019. (1/G')-Açılım Metodunu Kullanarak Sawada–Kotera Denkleminin Hiperbolik Yürüyen Dalga Çözümleri. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, 19, 3, 615-619.
  • Durur, H., Yokuş, A., 2020. Analytical solutions of Kolmogorov–Petrovskii–Piskunov equation. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22, 2, 628- 636.
  • Durur, H., Ilhan, E., Bulut, H., 2020. Novel complex wave solutions of the (2+ 1)-dimensional hyperbolic nonlinear Schrödinger equation. Fractal and Fractional, 4, 3, 41.
  • Fernandez, A., Özarslan, M.A. and Baleanu, D., 2019. On fractional calculus with general analytic kernels. Applied Mathematics and Computation, 354, 248- 265.
  • Khater, M. M., Ghanbari, B., Nisar, K. S., Kumar, D., 2020. Novel exact solutions of the fractional Bogoyavlensky-Konopelchenko equation involving the Atangana-Baleanu-Riemann derivative. Alexandria Engineering Journal, 59, 5, 2957-2967.
  • Kudryashov, N. A., 2005. Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos Solitons and Fractals, 24, 1217- 1231.
  • Kudryashov, N. A., 2005. Exact solitary waves of the Fisher equation. Physics Letters A, 342, 99-106.
  • Manafian, J., Lakestani, M., and Bekir, A., 2016. Study of the analytical treatment of the (2+ 1)-dimensional Zoomeron, the Duffing and the SRLW equations via a new analytical approach. International Journal of Applied and Computational Mathematics, 2, 2, 243- 268.
  • Morales-Delgado, V.F., Gomez-Aguilar, J.F., TanecoHernandez, M. A., and Baleanu, D., 2018. Modeling the fractional non-linear Schrödinger equation via Liouville-Caputo fractional derivative. Optik, 162, 1-7.
  • Özpınar, F., 2020. Kesirli Mertebe Kısmi Diferensiyel Denklemlerin Ayrık Homotopi Perturbasyon Metodu ile Çözümü. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 20, 2, 213-221.
  • Park, C., Khater, M. M., Abdel-Aty, A. H., Attia, R. A., Rezazadeh, H., Zidan, A. M., Mohamed, A. B. 2020. Dynamical analysis of the nonlinear complex fractional emerging telecommunication model with higher–order dispersive cubic–quintic. Alexandria Engineering Journal, 59, 3, 1425-1433.
  • Podlubny I., 1999. Fractional differential equations. Academic Press, San Diego.
  • Rezazadeh, H., Khodadad, F. S. and Manafian, J., 2017. New structure for exact solutions of nonlinear time fractional Sharma-Tasso-Olver equation via conformable fractional derivative. Applications and Applied Mathematics: An International Journal, 12, 1, 13-21.
  • Ray, S.S., 2006. Exact solutions for time-fractional diffusion-wave equations by decomposition method. Physica Scripta, 75, 1, 53.
  • Shang, N., Zheng, B., 2013. Exact solutions for three fractional partial differential equations by the (𝐺 ′/𝐺) method. International Journal of Applied Mathematics, 43, 3, 114-119.
  • Tasbozan, O., Kurt, A., Durur, H., 2019. Implementation of new sub equation method to time fractional partial differential equations. International Journal of Engineering Mathematics and Physics, 1, 1-12.
  • Yasar, E., Yıldırım, Y. , 2018. On the Lie symmetry analysis and traveling wave solutions of time fractional fifth-order modified Sawada-Kotera equation. Karaelmas Science and Engineering Journal, 8, 2, 411-416.
  • Yokuş, A., 2020. On the exact and numerical solutions to the FitzHugh–Nagumo equation. International Journal of Modern Physics B, 34, 17, 2050149.
  • Yokus, A., Durur, H., Ahmad, H., Yao, S. W., 2020. Construction of different types analytic solutions for the Zhiber-Shabat equation. Mathematics, 8, 6, 908.
  • Yokus, A., Durur, H., Ahmad, H., 2020. Hyperbolic type solutions for the couple Boiti-Leon-Pempinelli system. Facta Universitatis, Series: Mathematics and Informatics, 35, 2, 523-531.
  • Yokuş, A., Durur, H., Abro, K. A., Kaya, D., 2020. Role of Gilson–Pickering equation for the different types of soliton solutions: a nonlinear analysis. The European Physical Journal Plus, 135, 8, 1-19.
  • Yokuş, A., Durur, H., Nofal, T. A., Abu-Zinadah, H., Tuz, M., Ahmad, H., 2020. Study on the applications of two analytical methods for the construction of traveling wave solutions of the modified equal width equation. Open Physics, 18, 1, 1003-1010.
  • Zayed, E. M. E., Alurrfi, K. A. E., 2015. A new Jacobi elliptic function expansion method for solving a nonlinear PDE describing the nonlinear low-pass electrical lines. Chaos, Solitons, Fractals, 78, 148-155.
APA ÖZKAN Y (2021). Constructions Of Traveling Wave Solutions Of The Fractional NonlinearModel Of The Low-Pass Electrical Transmission Lines. , 496 - 506. 10.35414/akufemubid.860771
Chicago ÖZKAN Yeşim SAĞLAM Constructions Of Traveling Wave Solutions Of The Fractional NonlinearModel Of The Low-Pass Electrical Transmission Lines. (2021): 496 - 506. 10.35414/akufemubid.860771
MLA ÖZKAN Yeşim SAĞLAM Constructions Of Traveling Wave Solutions Of The Fractional NonlinearModel Of The Low-Pass Electrical Transmission Lines. , 2021, ss.496 - 506. 10.35414/akufemubid.860771
AMA ÖZKAN Y Constructions Of Traveling Wave Solutions Of The Fractional NonlinearModel Of The Low-Pass Electrical Transmission Lines. . 2021; 496 - 506. 10.35414/akufemubid.860771
Vancouver ÖZKAN Y Constructions Of Traveling Wave Solutions Of The Fractional NonlinearModel Of The Low-Pass Electrical Transmission Lines. . 2021; 496 - 506. 10.35414/akufemubid.860771
IEEE ÖZKAN Y "Constructions Of Traveling Wave Solutions Of The Fractional NonlinearModel Of The Low-Pass Electrical Transmission Lines." , ss.496 - 506, 2021. 10.35414/akufemubid.860771
ISNAD ÖZKAN, Yeşim SAĞLAM. "Constructions Of Traveling Wave Solutions Of The Fractional NonlinearModel Of The Low-Pass Electrical Transmission Lines". (2021), 496-506. https://doi.org/10.35414/akufemubid.860771
APA ÖZKAN Y (2021). Constructions Of Traveling Wave Solutions Of The Fractional NonlinearModel Of The Low-Pass Electrical Transmission Lines. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, 21(2), 496 - 506. 10.35414/akufemubid.860771
Chicago ÖZKAN Yeşim SAĞLAM Constructions Of Traveling Wave Solutions Of The Fractional NonlinearModel Of The Low-Pass Electrical Transmission Lines. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 21, no.2 (2021): 496 - 506. 10.35414/akufemubid.860771
MLA ÖZKAN Yeşim SAĞLAM Constructions Of Traveling Wave Solutions Of The Fractional NonlinearModel Of The Low-Pass Electrical Transmission Lines. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, vol.21, no.2, 2021, ss.496 - 506. 10.35414/akufemubid.860771
AMA ÖZKAN Y Constructions Of Traveling Wave Solutions Of The Fractional NonlinearModel Of The Low-Pass Electrical Transmission Lines. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi. 2021; 21(2): 496 - 506. 10.35414/akufemubid.860771
Vancouver ÖZKAN Y Constructions Of Traveling Wave Solutions Of The Fractional NonlinearModel Of The Low-Pass Electrical Transmission Lines. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi. 2021; 21(2): 496 - 506. 10.35414/akufemubid.860771
IEEE ÖZKAN Y "Constructions Of Traveling Wave Solutions Of The Fractional NonlinearModel Of The Low-Pass Electrical Transmission Lines." Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, 21, ss.496 - 506, 2021. 10.35414/akufemubid.860771
ISNAD ÖZKAN, Yeşim SAĞLAM. "Constructions Of Traveling Wave Solutions Of The Fractional NonlinearModel Of The Low-Pass Electrical Transmission Lines". Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 21/2 (2021), 496-506. https://doi.org/10.35414/akufemubid.860771