Solutions of Time Fractional Mathematical Model with Effective Techniques

Year 2023, Volume: 13 Issue: 2, 203 - 220, 31.12.2023

Yusuf Gürefe , Yusuf Pandir , Tolga Aktürk

https://doi.org/10.54370/ordubtd.1324572

Abstract

In this article, the Time Fractional Clannish Random Walker’s Parabolic Equation traveling wave solutions,a non-linear partial differential equation, is analyzed using the modified exponential function method (MEFM) and the Generalized Kudryashov Method (GKM). In this way, the solution functions of the mathematical model were obtained through a mathematical program with the help of two effective methods. Two-dimensional, three-dimensional, contour graphics simulating the behavior of this non-linear mathematical model were drawn with the help of the program under appropriate parameters.

Keywords

the time fractional Clannish Random Walker’s parabolic equation, modified exponential function method, generalized Kudryashov method

Zaman Kesirli Matematiksel Modelin Etkili Tekniklerle Çözümü

Abstract

Bu makalede, doğrusal olmayan bir kısmi diferansiyel denklem olan Zaman Kesirli Clannish Random Walker'ın Parabolik Denklemi hareketli dalga çözümleri, Geliştirilmiş Üstel Fonksiyon Metodu (GÜFM) ve Genelleştirilmiş Kudryashov Metodu (GKM) kullanılarak analiz edilmektedir. Bu şekilde, matematiksel modelin çözüm fonksiyonları, iki etkili yöntem yardımıyla matematiksel bir program aracılığıyla elde edilmiştir. Doğrusal olmayan bu matematiksel modelin davranışını simüle eden iki boyutlu, üç boyutlu kontur grafikleri program yardımıyla uygun parametreler altında çizilmiştir.

Keywords

zaman kesirli Clannish Random Walker, geliştirilmiş üstel fonksiyon metodu, genelleştirilmiş Kudryashov metodu

References

• Akbar, M. A., Akinyemi, L., Yao, S. W., Jhangeer, A., Rezazadeh, H., Khater, M. M., & Inc, M. (2021). Soliton solutions to the Boussinesq equation through sine-Gordon method and Kudryashov method. Results in Physics, 25, 104228. https://doi.org/10.1016/j.rinp.2021.104228
• Baskonus, H. M., & Hasan B. (2015). An effective schema for solving some nonlinear partial differential equation arising in nonlinear physics. Open Physics, 13, 280-289. https://doi.org/10.1515/phys-2015-0035
• Bulut, H., Akkilic, A. N., & Khalid, B. J. (2021). Soliton solutions of hirota equation and Hirota-Maccari System by the (M+ 1/G')-expansion method. Advanced Mathematical Models & Applications, 6(1). http://dx.doi.org/10.20852/ntmsci.2019.348
• Ebadi, G., & Biswas, A. (2011). The G′/G method and 1-soliton solution of the Davey–Stewartson equation. Mathematical and Computer Modelling, 53(5-6), 694-698. https://doi.org/10.1016/j.mcm.2010.10.005
• Ekici, M., Mirzazadeh, M., Sonmezoglu, A., Ullah, M. Z., Zhou, Q., Moshokoa, S. P., & Belic, M. (2017a). Nematicons in liquid crystals by extended trial equation method. Journal of Nonlinear Optical Physics & Materials, 26(01), 1750005. https://doi.org/10.1007/s11082-019-1813-0
• Ekici, M., Mirzazadeh, M., Sonmezoglu, A., Ullah, M. Z., Zhou, Q., Triki, H., & Biswas, A. (2017b). Optical solitons with anti-cubic nonlinearity by extended trial equation method. Optik, 136, 368-373. https://doi.org/10.1016/j.ijleo.2019.03.141
• Ergün, A. & Amirov, R. Kh. (2022). Half inverse problem for diffusion operators with jump conditions dependent on the spectral parameter. Numerical Methods for Partial Differential Equations, 38(3), 577–590. https://doi.org/10.1002/num.22666
• Ergun, A. (2020a). The multiplicity of eigenvalues of a vectorial diffusion equations with discontinuous function inside a finite interval. Turkish Journal of Science, 5(2), 73-85. https://dergipark.org.tr/en/download/article-file/1159115
• Ergun, A. (2020b). A half inverse problem for the singular diffusion operator with jump condition. Miskolch Mathematical Notes, 21(2), 805-821. https://doi.org/10.48550/arXiv.2006.08329
• Ghanbari, B., & Gómez-Aguilar, J. F. (2019). The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with β-conformable time derivative. Revista Mexicana de Física, 65(5), 503-518. https://doi.org/10.31349/RevMexFis.65.503
• He, J. H., & Wu, X. H. (2006). Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals, 30(3), 700-708. https://doi.org/10.1016/j.chaos.2006.03.020
• Kaplan, M., & Akbulut, A., The analysis of the soliton-type solutions of conformable equations by using generalized Kudryashov method, Optical and Quantum Electronics, 53(9), 1-21. https://doi.org/10.21203/rs.3.rs-315162/v1
• Kudryashov, N. A. (2010). A note on the G′/G-expansion method. Applied Mathematics and Computation, 217(4), 1755-1758. http://dx.doi.org/10.1016/j.amc.2010.03.071
• Siddique, I., Mehdi, K. B., Akbar, M. A., Khalifa, H. A. E. W., & Zafar, A. (2022). Diverse exact soliton solutions of the time Fractional Clannish Random Walker’s Parabolic Equation via Dual Novel Techniques. Journal of Function Spaces, 2022, 1680560. https://doi.org/10.1155/2022/1680560
• Yel, G., Baskonus, H. M., & Bulut, H. (2017). Novel archetypes of new coupled Konno–Oono equation by using sine-Gordon expansion method. Optical and Quantum Electronics, 49, 1-10. https://doi.org/10.1007/s11082-017-1127-z
• Zayed, E. M., & Gepreel, K. A. (2009). Some applications of the G′/G-expansion method to non-linear partial differential equations. Applied Mathematics and Computation, 212(1), 1-13. https://doi.org/10.1016/j.amc.2009.02.009
• Zheng, B. (2014). A new variable-coefficient bernoulli equation-based sub-equation method for solving nonlinear differential equations. University Politehnica Of Bucharest Scientific Bulletin-Series A-Applied Mathematics And Physics, 76(2), 63-74. https://www.scientificbulletin.upb.ro/rev_docs_arhiva/fullf78_932361.pdf
• Zhou, Q. (2014). Analytical solutions and modulation instability analysis to the perturbed nonlinear Schrödinger equation. Journal of Modern Optics, 61(6), 500-503. https://doi.org/10.1080/09500340.2014.897391