SavedAdd your journal

Journals / Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi / 2023 / Cilt: 39 Sayı: 2

The New Conformable Methods to Solve Conformable Time- Fractional Generalized Burgers Equation with Proportional Delay

Oransal Gecikmeli Uyumlu Zaman-Kesirli Mertebeden Genelleştirilmiş Burgers Denklemini Çözmek için Yeni Uyumlu Metotlar

Halil Hüseyin AVCI
Halil ANAÇ
Pages
315–329
Publication Date
2023-08-31
DOI
—
🏛️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)

When the exact solutions are compared to the solutions that were found, it is seen that both of the new techniques are simple, powerful, and work well to solve nonlinear conformable time-fractional partial differential equation with proportional delay.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, two novel methods called conformable q-Mohand homotopy analysis transform method (Cq-MHATM) and conformable Mohand Adomian decomposition method (CMADM) are utilized to examine the novel numerical solutions for nonlinear conformable time-fractional generalized Burgers equation with proportional delay.
📊
Key Findings & Data:The first of the two new methods proposed, Cq-MHATM, is a hybrid method that combines q-homotopy analysis transform method and Mohand transform in the sense of comformable derivative.
💡
Conclusion & Impact:When the exact solutions are compared to the solutions that were found, it is seen that both of the new techniques are simple, powerful, and work well to solve nonlinear conformable time-fractional partial differential equation with proportional delay.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Uyumlu zaman-kesirli mertebeden genelleştirilmiş Burgers denklemi · Uyumlu Mohand Adomian ayrıştırma metodu · Uyumlu Mohand dönüşümü

Abstract

In this article, two novel methods called conformable q-Mohand homotopy analysis transform method (Cq-MHATM) and conformable Mohand Adomian decomposition method (CMADM) are utilized to examine the novel numerical solutions for nonlinear conformable time-fractional generalized Burgers equation with proportional delay. The first of the two new methods proposed, Cq-MHATM, is a hybrid method that combines q-homotopy analysis transform method and Mohand transform in the sense of comformable derivative. The other method, CMADM is also a hybrid method that combines Adomian decomposition method and Mohand transform in the sense of comformable derivative. The computer simulations were worked out to prove that the proposed methods work and are trusted. When the exact solutions are compared to the solutions that were found, it is seen that both of the new techniques are simple, powerful, and work well to solve nonlinear conformable time-fractional partial differential equation with proportional delay.

Özet

Bu makalede, uyumlu q-Mohand homotopi analiz dönüşüm yöntemi (Uq-MHADY) ve uyumlu Mohand Adomian ayrıştırma yöntemi (UMAAY) olarak adlandırılan iki yeni yöntem, oransal gecikmeli doğrusal olmayan uyumlu zaman-kesirli mertebeden genelleştirilmiş Burgers denkleminin yeni sayısal çözümlerini incelemek için kullanılmaktadır. Önerilen iki yeni yöntemden ilki olan Uq-MHADY, q-homotopi analiz dönüşüm yöntemi ile uyumlu Mohand dönüşümünün birleşiminden oluşan hibrit bir yöntemdir. Diğer yöntem olan CMADM ise Adomian ayrıştırma yöntemi ile uyumlu Mohand dönüşümünün birleşiminden oluşan hibrit bir yöntemdir. Önerilen yöntemlerin etkin çalıştığını ve güvenilir olduğunu göstermek için bilgisayar simülasyonları yapılmaktadır. Kesin çözümler bulunan çözümlerle karşılaştırıldığında, yeni tekniklerin her ikisinin de basit, güçlü ve oransal gecikmeli doğrusal olmayan uyumlu zaman-kesirli mertebeden kısmi diferansiyel denklemi çözmek için iyi çalıştığını görülmektedir.

🔖

Cite This Article

AVCI, H. H., ANAÇ, H. (2023). The New Conformable Methods to Solve Conformable Time- Fractional Generalized Burgers Equation with Proportional Delay. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, Cilt: 39 Sayı: 2, 315–329. https://ajindex.com/articles/960420

📄 Full Text PDF Viewer

↗New Tab

References (1)

  1. [1] Miller, K. S., Ross, B. 1993. An introduction to the fractional calculus and fractional differential equations, Wiley, New York, 376 p. [2] Podlubny, I. 1999. Fractional differential equations, mathematics in science and engineering, Academic Press, New York, 365 p. [3] Baleanu, D., Diethelm, K., Scalas, E., Trujillo, J. J. 2012. Fractional calculus: models and numerical methods, World Scientific, London, 476 p. [4] Povstenko, Y. 2015. Linear fractional diffusion-wave equation for scientists and engineers. Birkhäuser, Switzerland, 460 p. [5] Ala, V. 2022. New exact solutions of space-time fractional Schrödinger-Hirota equation. Bulletin of the Karaganda university Mathematics series, 107(3), 17-24. [6] Ala, V. 2023. Exact Solutions of Nonlinear Time Fractional Schrödinger Equation with Beta- Derivative. Fundamentals of Contemporary Mathematical Sciences, 4(1), 1-8. [7] Baleanu, D., Wu, G. C., Zeng, S. D. 2017. Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations. Chaos, Solitons & Fractals, 102, 99-105. [8] Sweilam, N. H., Abou Hasan, M. M., Baleanu, D. 2017. New studies for general fractional financial models of awareness and trial advertising decisions. Chaos, Solitons & Fractals, 104, 772-784. [9] Liu, D. Y., Gibaru, O., Perruquetti, W., Laleg-Kirati, T. M. 2015. Fractional order differentiation by integration and error analysis in noisy environment. IEEE Transactions on Automatic Control, 60(11), 2945-2960. [10] Esen, A., Sulaiman, T. A., Bulut, H., Baskonus, H. M. 2018. Optical solitons to the space-time fractional (1+1)- dimensional coupled nonlinear Schrödinger equation. Optik, 167, 150-156. [11] Veeresha, P., Prakasha, D. G., Baskonus, H. M. 2019. Novel simulations to the time-fractional Fisher’s equation. Mathematical Sciences, 13(1), 33-42. [12] Veeresha, P., Prakasha, D. G., Baskonus, H. M. 2019. New numerical surfaces to the mathematical model of cancer chemotherapy effect in Caputo fractional derivatives. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29(1), 013119. [13] Caponetto, R., Dongola, G., Fortuna, L., Gallo, A. 2010. New results on the synthesis of FO-PID controllers. Communications in Nonlinear Science and Numerical Simulation, 15(4), 997-1007. [14] Prakash, A., Veeresha, P., Prakasha, D. G., Goyal, M. 2019. A homotopy technique for a fractional order multi-dimensional telegraph equation via the Laplace transform. The European Physical Journal Plus, 134, 1-18. [15] Mohand, M.