THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Zeliha Körpinar

,

Talat Korpinar

,

Mustafa Inc

OPTICAL MODELLING OF THE SPACE-TIME FRACTIONAL ECKHAUS EQUATION

ABSTRACT
In this paper, the space-time fractional Eckhaus equation is considered and solved using the a direct method (Khater method) to obtain exact solutions. This meth­od produces more solutions when compared to other known methods. The real solutions of this equation are classified as travelling wave, kink, periodic and sol­itary wave solutions. These solutions are searched with the help of the fractional conformable derivative sense. Some graphs and tables are drawn to interpret the solutions and method. With the interpretation of the results, it is explained that the method used is a reliable, effective, powerful and easily applicable technique for obtaining the solutions of fractional differential equations classes in many fields.
KEYWORDS
conformable derivative, the space-time fractional Eckhaus equation, Khater method
PAPER SUBMITTED: 2022-07-11
PAPER REVISED: 2022-07-24
PAPER ACCEPTED: 2022-08-01
PUBLISHED ONLINE: 2023-04-08
DOI REFERENCE: https://doi.org/10.2298/TSCI23S1389K
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Special issue 1, PAGES [389 - 399]
REFERENCES
  1. Kilbas, A. A., et al., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, The Netherlands, 2006
  2. Podlubny, I., Fractional Differential Equation, Academic Press, San Diego, USA, 1999
  3. Sabatier, J., et al., (Eds.), Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, Germany, 2007
  4. Samko, S. G., et al., Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Switzerland, 1993
  5. Wu, G. C., et al., Fractional Impulsive Differential Equations: Exact Solutions, Integral Equations and Short Memory Case, Frac. Calc. Appl. Anal., 22 (2019), Mar., pp. 180-192
  6. Khater, M. M. A., et al., Elliptic and Solitary Wave Solutions for Bogoyavlenskii Equations System, Couple Boiti-Leon-Pempinelli Equations System and Time-fractional Cahn-Allen Equation, Results in Physics, 7 (2017), July, pp. 2325-2333
  7. Khan, M.M., et al., Traveling Wave Solutions for Space-Time Fractional Cahn Hilliard Equation and Space-Time Fractional Symmetric Regularized Long-Wave Equation, Alexandria Engineering Journal, 60 (2021), 1, pp. 1317-1324
  8. Ali, M., et al., Explicit and Approximate Solutions for the Conformable-Caputo Time-Fractional Diffusive Predator-Prey Model, Int. J. Appl. Comput. Math., 7 (2021), 90
  9. Kadkhoda, N., Jafari, H., An Analytical Approach to Obtain Exact Solutions of Some Space-Time Conformable Fractional Differential Equations, Advances in Difference Equations, 2019 (2019), 428
  10. Taghizadeh, N., et al., The First Integral Method Applied to the Eckhaus Equation, Appl. Math. Lett., 25 (2012), 5, pp. 798-802
  11. Calogero, F., Lillo, S. D., The Eckhaus PDE iФt + фxx + 2ф|ф|2x + ф| ф |4 = 0, Inverse Probl., 3 (1987), 4, pp. 633-681
  12. Khalil, R., et al., A New Definition of Fractional Derivative, Journal of Computational and Applied Mathematics, 264 (2014), July, pp. 65-70
  13. Eslami, M., Rezazadeh, H., The First Integral Method for Wu-Zhang System with Conformable Time-Fractional Derivative, Calcolo, 53 (2016), Oct., pp. 475-485
  14. Korpinar, Z., et al., New Soliton Solutions of the Fractional Regularized Long Wave Burger Equation by Means of Conformable Derivative, Results in Physics, 14 (2019), 102395
  15. Z, Korpinar, T., New Optical Hybrid Electromotive of B2-Ferromagnetic Fiber with some Optical Applications, Optik, 251 (2022), 168190
  16. Korpinar, T., et al., Optical Quasi Flux Density of Heisenberg Ferromagnetic Spin with qHATM Approach, Optik, 245 (2021), 16756
  17. Bibi, S., et al., Khater Method for Non-Linear Sharma Tasso-Olever (STO) Equation of Fractional Order, Results in Physics, 7 (2017), Nov., pp. 4440-4450
  18. Abdelrahman, M. A. E., et al., Exact Solutions of the Cubic Boussinesq and Coupled Higgs System, Thermal Science, 24 (2020), Suppl. 1, pp. S333-S342
  19. Aliyu, A.I., et al., Adomian-Pade Approximate Solutions to the Conformable Non-Linear Heat Transfer Equation, Thermal Science, 23 (2019), Suppl. 1, pp. S235-S242
  20. Aliyu, A. I., et al., Approximate Solutions and Conservation Laws of the Periodic Base Temperature of Convective Longitudinal Fins in Thermal Conductivity, Thermal Science, 23 (2019), Suppl. 1, pp. S267-S273
PDF VERSION [DOWNLOAD]
Optical modelling of the space-time fractional Eckhaus equation

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence