Araştırma Makalesi
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Solutions of Time Fractional Mathematical Model with Effective Techniques

Yıl 2023, Cilt: 13 Sayı: 2, 203 - 220, 31.12.2023
https://doi.org/10.54370/ordubtd.1324572

Öz

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.

Kaynakça

  • 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

Zaman Kesirli Matematiksel Modelin Etkili Tekniklerle Çözümü

Yıl 2023, Cilt: 13 Sayı: 2, 203 - 220, 31.12.2023
https://doi.org/10.54370/ordubtd.1324572

Öz

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.

Kaynakça

  • 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

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik (Diğer)
Bölüm Araştırma Makaleleri
Yazarlar

Yusuf GÜREFE 0000-0002-7210-5683

Yusuf PANDİR 0000-0003-0274-7901

Tolga AKTÜRK 0000-0002-8873-0424

Erken Görünüm Tarihi 29 Aralık 2023
Yayımlanma Tarihi 31 Aralık 2023
Gönderilme Tarihi 8 Temmuz 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 13 Sayı: 2

Kaynak Göster

APA GÜREFE, Y., PANDİR, Y., & AKTÜRK, T. (2023). Solutions of Time Fractional Mathematical Model with Effective Techniques. Ordu Üniversitesi Bilim Ve Teknoloji Dergisi, 13(2), 203-220. https://doi.org/10.54370/ordubtd.1324572