Exact analytical solutions of the fractional biological population model, fractional EW and modified EW equations

Authors

  • Meryem Odabaşı Ege University

DOI:

https://doi.org/10.11121/ijocta.01.2021.00841

Keywords:

Fractional differential equations, conformable derivative, exact traveling wave solutions

Abstract

In this paper, exact analytical solutions of the biological population model, the EW and the modified EW equations with a conformable derivative operator have been examined by means of the trial solution algorithm and the complete discrimination system. Dark, bright and singular traveling wave solutions of the equations have been obtained by algorithm. Also, revealed singular periodic solutions have been listed. All solutions were verified by substituting them into their corresponding equation via Mathematica package program.

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References

El-Sayed, A.M.A., Rida, S.Z., Arafa, A.A.M. (2009). Exact solutions of fractional-order biological population model. Communications in Theoretical Physics, 52, 992–996.

Bekir, A., Güner, Ö., Cevikel, A.C. (2013). Fractional complex transform and exp-function methods for fractional differential equations. Abstract and Applied Analysis, Article ID 426462, 8 pages, DOI: 10.1155/2013/426462.

Kumar, D., Seadawy, A.R., Joardar, A.K. (2018). Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology. Chinese Journal of Physics, 56, 75–85.

Meng, F. (2013). A New Approach for solving fractional partial differential equations. Journal of Applied Mathematics, Article ID 256823, 5 pages, DOI: 10.1155/2013/256823.

Hosseini, K., Ayati, Z. (2016). Exact solutions of space-time fractional EW and modified EW equations using Kudryashov method. Nonlinear Science Letters A,7 (2), 58–66.

Guner, O., Bekir, A. (2017). A novel method for nonlinear fractional differential equations using symbolic computation. Waves in Random and Complex Media, 27(1), 163–170.

Caputo, M., Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications, 1(2), 73–85.

Shadab, M., Faisal Khan, M., Luis Lopez-Bonilla, J. (2018). A new Riemann–Liouville type fractional derivative operator and its application in generating functions. Advances in Difference Equations, 167.

Khalil, R., Horani, M.A., Sababheh A.M.Y. (2014). A new definition of fractional derivative. Journal of Computational and Applied Mathematics ,264, 65–70.

Abdeljawad, T. (2015). On conformable fractional calculus. Journal of Computational and Applied Mathematics, 279, 57–66.

Hosseini, K., Korkmaz, A., Bekir, A., Samadani, F., Zabihi, A., Topsakal, M. (2019). New wave form solutions of nonlinear conformable time-fractional Zoomeron equation in (2?+?1)-dimensions. Waves in Random and Complex Media, DOI: 10.1080/17455030.2019.1579393.

Hosseini, K., Manafian, J., Samadani, F., Foroutan, M., Mirzazadeh, M., Zhou, Q. (2018). Resonant optical solitons with perturbation terms and fractional temporal evolution using improved tan (?(?)/2)-expansion method and exp function approach. Optik, 158, 933–939.

Hosseini, K., Mayeli, P., Bekir, A., Guner, O. (2018). Density-dependent conformable space-time fractional diffusion-reaction equation and its exact solutions. Communications in Theoretical Physics, 69, 1–4.

Odabasi, M., Pinar, Z., Kocak, H. (2020). Analytical solutions of some nonlinear fractional-order differential equations by different methods. Mathematical Methods in the Applied Sciences, DOI: 10.1002/mma.6313.

Hosseini, K., Bekir, A., Kaplan, M., Guner, O. (2017). On a new technique for solving the nonlinear conformable time-fractional differential equations. Optical and Quantum Electronics, 49, 343.

Hosseini, K., Bekir, A., Ansari, R. (2017). Exact solutions of nonlinear conformable time-fractional Boussinesq equations using the exp(??(?))-expansion method. Optical and Quantum Electronics, 49, 131.

Liu, C.S. (2006). Trial equation method to nonlinear evolution equations with rank inhomogeneous: mathematical discussions and its applications. Communications in Theoretical Physics, 45, 219–223.

Liu, C.S. (2006). A New trial equation method and its applications. Communications in Theoretical Physics, 45, 395–397.

Liu, C.S. (2010). Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations. Computer Physics Communications, 181, 317–324.

Biswas, A. (2018). Optical solitons with differential group delay for coupled Fokas–Lenells equation by extended trial function scheme. Optik, 165, 102–110.

Odabasi, M., Misirli, E. (2017). A note on the traveling wave solutions of some nonlinear evolution equations. Optik, 142, 394–400.

Odabasi, M., Misirli, E. (2018). On the solutions of the nonlinear fractional differential equations via the modifed trial equation method. Mathematical Methods in the Applied Sciences, 41, 904–911.

Odabasi, M. (2020). Traveling wave solutions of conformable time-fractional Zakharov–Kuznetsov and Zoomeron equations. Chinese Journal of Physics, 64, 194–202.

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Published

2020-12-17
CITATION
DOI: 10.11121/ijocta.01.2021.00841
Published: 2020-12-17

How to Cite

Odabaşı, M. (2020). Exact analytical solutions of the fractional biological population model, fractional EW and modified EW equations. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 11(1), 52–58. https://doi.org/10.11121/ijocta.01.2021.00841

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Research Articles