Research Article
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A new analytical approach to the (1+1)-dimensional conformable Fisher equation

Year 2022, , 211 - 220, 30.12.2022
https://doi.org/10.53391/mmnsa.2022.017

Abstract

In this paper, we use an effective method which is the rational sine-Gordon expansion method to present new wave simulations of a governing model. We consider the (1+1)-dimensional conformable Fisher equation which is used to describe the interactive relation between diffusion and reaction. Various types of solutions such as multi-soliton, kink, and anti-kink wave soliton solutions are obtained. Finally, the physical behaviours of the obtained solutions are shown by 3D, 2D, and contour surfaces.

References

  • Cooper, F., Khare, A., Mihaila, B., & Saxena, A. Exact solitary wave solutions for a discrete λφ4 field theory in (1+1)-dimensions. Physical Review E, 72(3), 036605, (2005).
  • Hirota, R. Exact solution of the Korteweg–de Vries equation for multiple collision of solitons. Physical Review Letters, 27(18), 1192–1194, (1971).
  • Malfliet, W. Solitary wave solutions of nonlinear wave equations. American Journal of Physics, 60(7), 650–654, (1992).
  • Fan, E. Extended tanh-function method and its applications to nonlinear equations. Physics Letters A, 277(4-5), 212–218, (2000).
  • Ma, W.X., Huang T., & Zhang, Y. A multiple exp-function method for nonlinear differential equations and its application. Physica Scripta, 82(6), 065003, (2010).
  • Ma, W.X., & Lee, J.H. A transformed rational function method and exact solutions to the (3+1)-dimensional Jimbo–Miwa equation. Chaos, Solitons & Fractals, 42(3), 1356–1363, (2009).
  • Feng, Z.S., & Wang, X.H. The first integral method to the two dimensional Burgers–Korteweg–de Vries equation. Physics Letters A, 308(2-3), 173–178, (2003).
  • Jawad, A.J.A.M., Petkovic, M.D., & Biswas, A. Modified simple equation method for nonlinear evolution equations. Applied Mathematics and Computation, 217(2), 869–877, (2010).
  • Aksan, E.N., Bulut, H., & Kayhan, M. Some wave simulation properties of the (2+1) dimensional breaking soliton equation. ITM Web of Conferences, 13, 01014, (2017).
  • Bulut, H., Aksan, E.N., Kayhan, M., & Sulaiman, T.A. New solitary wave structures to the (3+1) dimensional Kadomtsev–Petviashvili and Schrödinger equation. Journal of Ocean Engineering and Science, 4(4), 373-378, (2019).
  • Yel, G., Baskonus, H.M., & Bulut, H. Novel archetypes of new coupled Konno-Oono equation by using sine-Gordon expansion method. Optical and Quantum Electronics, 49(9), 285, (2017).
  • Yan, L., Baskonus, H.M., Cattani, C., & Gao, W. Extractions of the gravitational potential and high-frequency wave Perturbation properties of nonlinear (3+1)- dimensional Vakhnenko-Parkes equation via novel approach. Mathematical Methods in the Applied Sciences, 1-10, (2022).
  • Chen, Q., Baskonus, H.M., Gao, W., & Ilhan, E. Soliton theory and modulation instability analysis: The Ivancevic option pricing model in economy. Alexandria Engineering Journal, 61(10), 7843-7851, (2022).
  • Veeresha, P., Yavuz, M., & Bhaishya, C. A computational approach for shallow water forced Korteweg-De Vries equation on critical flow over a hole with three fractional operators. An International Journal of Optimization and Control: Theories & Applications, 11(3), 52-67, (2021).
  • Jayaprakasha, P.C., & Bhaishya, C. Numerical analysis of predator-prey model in presence of toxicant by a novel approach. Mathematics in Computer Science, 11(4), 3963-3983, (2021).
  • Bhaishya, C. A new application of Hermite collocation method. International Journal of Mathematical, Engineering and Management Sciences, 14(1), 182-190, (2019).
  • Bhaishya, C., & Jaipala. Comparative study of homotopy perturbation method and Genocchi polynomial method for first order fractional differential equation. Journal of Computer and Mathematical Sciences, 10(1), 197-206, (2019).
  • Bhaishya, C., & Veeresha, P. Laguerre polynomial-based operational matrix of integration for solving fractional differential equations with non-singular kernel. Proceedings of the Royal Society A, 477(2253), 20210438, (2021).
  • Zhou, Q., Ekici M., Sonmezoglu, A., Manafian, J., Khaleghizadeh, S., & Mirzazadeh, M. Exact solitary wave solutions to the generalized Fisher equation. Optik, 127(24), 12085-12092, (2016).
  • Fisher, R.A. The advance of advantageous genes. Annals of Eugenics, 7(4), 355-369, (1937).
  • Wazwaz, A.M. The extended tanh method for abundant solitary wave solutions of nonlinear wave equations. Applied Mathematics and Computation, 187(2), 1131-1142, (2007).
  • Triki, H., & Wazwaz, A.M. Trial equation method for solving the generalized Fisher equation with variable coefficients. Physics Letters A, 380(13), 1260-1262, (2016).
  • Matinfar, M., Bahar, S.R., & Ghasemi, M. Solving the Generalized Fisher’s equation by differential transform method. Journal of Applied Mathematics and Informatics, 30(3-4), 555–560, (2012).
  • Khalil, R., Al Horani, M., Yousef, A., & Sababheh, M. A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264, 65–70, (2014).
  • Atangana, A., Baleanu, D., & Alsaedi, A. New properties of conformable derivative. Open Mathematics, 13(1), 889–898, (2015).
  • Yan, L., Yel, G., Baskonus, H.M., Bulut, H., & Gao, W. Newly developed analytical method and its applications of some mathematical models. International Journal of Modern Physics B, 36(04), 2250040, (2022).
  • Yan, L., Yel, G., Kumar, A., Baskonus, H.M., & Gao, W. Newly developed analytical scheme and its applications to the some nonlinear partial differential equations with the conformable derivative. Fractal and Fractional, 5(4), 238, 1-15, (2021).
  • Yamgoué, S.B., Deffo, G.R., & Pelap, F.B. A new rational sine-Gordon expansion method and application to nonlinear wave equations arising in mathematical physics. The European Physical Journal Plus, 134(8), 380, (2019).
  • Tyson, J.J., & Brazhnik, P.K. On travelling wave solutions of Fisher’s equation in two spatial dimensions. SIAM Journal on Applied Mathematics, 60(2), 371-391, (2000).
  • Murray, J.D. Mathematical Biology: I. An Introduction (3rd Edition). Springer (2002).
  • Veeresha, P., Prakasha, D.G., & Baskonus, H.M. Novel simulations to the time fractional Fisher’s equation. Mathematical Sciences, 13(1), 33-42, (2019).
Year 2022, , 211 - 220, 30.12.2022
https://doi.org/10.53391/mmnsa.2022.017

Abstract

References

  • Cooper, F., Khare, A., Mihaila, B., & Saxena, A. Exact solitary wave solutions for a discrete λφ4 field theory in (1+1)-dimensions. Physical Review E, 72(3), 036605, (2005).
  • Hirota, R. Exact solution of the Korteweg–de Vries equation for multiple collision of solitons. Physical Review Letters, 27(18), 1192–1194, (1971).
  • Malfliet, W. Solitary wave solutions of nonlinear wave equations. American Journal of Physics, 60(7), 650–654, (1992).
  • Fan, E. Extended tanh-function method and its applications to nonlinear equations. Physics Letters A, 277(4-5), 212–218, (2000).
  • Ma, W.X., Huang T., & Zhang, Y. A multiple exp-function method for nonlinear differential equations and its application. Physica Scripta, 82(6), 065003, (2010).
  • Ma, W.X., & Lee, J.H. A transformed rational function method and exact solutions to the (3+1)-dimensional Jimbo–Miwa equation. Chaos, Solitons & Fractals, 42(3), 1356–1363, (2009).
  • Feng, Z.S., & Wang, X.H. The first integral method to the two dimensional Burgers–Korteweg–de Vries equation. Physics Letters A, 308(2-3), 173–178, (2003).
  • Jawad, A.J.A.M., Petkovic, M.D., & Biswas, A. Modified simple equation method for nonlinear evolution equations. Applied Mathematics and Computation, 217(2), 869–877, (2010).
  • Aksan, E.N., Bulut, H., & Kayhan, M. Some wave simulation properties of the (2+1) dimensional breaking soliton equation. ITM Web of Conferences, 13, 01014, (2017).
  • Bulut, H., Aksan, E.N., Kayhan, M., & Sulaiman, T.A. New solitary wave structures to the (3+1) dimensional Kadomtsev–Petviashvili and Schrödinger equation. Journal of Ocean Engineering and Science, 4(4), 373-378, (2019).
  • Yel, G., Baskonus, H.M., & Bulut, H. Novel archetypes of new coupled Konno-Oono equation by using sine-Gordon expansion method. Optical and Quantum Electronics, 49(9), 285, (2017).
  • Yan, L., Baskonus, H.M., Cattani, C., & Gao, W. Extractions of the gravitational potential and high-frequency wave Perturbation properties of nonlinear (3+1)- dimensional Vakhnenko-Parkes equation via novel approach. Mathematical Methods in the Applied Sciences, 1-10, (2022).
  • Chen, Q., Baskonus, H.M., Gao, W., & Ilhan, E. Soliton theory and modulation instability analysis: The Ivancevic option pricing model in economy. Alexandria Engineering Journal, 61(10), 7843-7851, (2022).
  • Veeresha, P., Yavuz, M., & Bhaishya, C. A computational approach for shallow water forced Korteweg-De Vries equation on critical flow over a hole with three fractional operators. An International Journal of Optimization and Control: Theories & Applications, 11(3), 52-67, (2021).
  • Jayaprakasha, P.C., & Bhaishya, C. Numerical analysis of predator-prey model in presence of toxicant by a novel approach. Mathematics in Computer Science, 11(4), 3963-3983, (2021).
  • Bhaishya, C. A new application of Hermite collocation method. International Journal of Mathematical, Engineering and Management Sciences, 14(1), 182-190, (2019).
  • Bhaishya, C., & Jaipala. Comparative study of homotopy perturbation method and Genocchi polynomial method for first order fractional differential equation. Journal of Computer and Mathematical Sciences, 10(1), 197-206, (2019).
  • Bhaishya, C., & Veeresha, P. Laguerre polynomial-based operational matrix of integration for solving fractional differential equations with non-singular kernel. Proceedings of the Royal Society A, 477(2253), 20210438, (2021).
  • Zhou, Q., Ekici M., Sonmezoglu, A., Manafian, J., Khaleghizadeh, S., & Mirzazadeh, M. Exact solitary wave solutions to the generalized Fisher equation. Optik, 127(24), 12085-12092, (2016).
  • Fisher, R.A. The advance of advantageous genes. Annals of Eugenics, 7(4), 355-369, (1937).
  • Wazwaz, A.M. The extended tanh method for abundant solitary wave solutions of nonlinear wave equations. Applied Mathematics and Computation, 187(2), 1131-1142, (2007).
  • Triki, H., & Wazwaz, A.M. Trial equation method for solving the generalized Fisher equation with variable coefficients. Physics Letters A, 380(13), 1260-1262, (2016).
  • Matinfar, M., Bahar, S.R., & Ghasemi, M. Solving the Generalized Fisher’s equation by differential transform method. Journal of Applied Mathematics and Informatics, 30(3-4), 555–560, (2012).
  • Khalil, R., Al Horani, M., Yousef, A., & Sababheh, M. A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264, 65–70, (2014).
  • Atangana, A., Baleanu, D., & Alsaedi, A. New properties of conformable derivative. Open Mathematics, 13(1), 889–898, (2015).
  • Yan, L., Yel, G., Baskonus, H.M., Bulut, H., & Gao, W. Newly developed analytical method and its applications of some mathematical models. International Journal of Modern Physics B, 36(04), 2250040, (2022).
  • Yan, L., Yel, G., Kumar, A., Baskonus, H.M., & Gao, W. Newly developed analytical scheme and its applications to the some nonlinear partial differential equations with the conformable derivative. Fractal and Fractional, 5(4), 238, 1-15, (2021).
  • Yamgoué, S.B., Deffo, G.R., & Pelap, F.B. A new rational sine-Gordon expansion method and application to nonlinear wave equations arising in mathematical physics. The European Physical Journal Plus, 134(8), 380, (2019).
  • Tyson, J.J., & Brazhnik, P.K. On travelling wave solutions of Fisher’s equation in two spatial dimensions. SIAM Journal on Applied Mathematics, 60(2), 371-391, (2000).
  • Murray, J.D. Mathematical Biology: I. An Introduction (3rd Edition). Springer (2002).
  • Veeresha, P., Prakasha, D.G., & Baskonus, H.M. Novel simulations to the time fractional Fisher’s equation. Mathematical Sciences, 13(1), 33-42, (2019).
There are 31 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Articles
Authors

Gülnur Yel 0000-0002-5134-4431

Miraç Kayhan This is me 0000-0003-1603-1891

Armando Ciancio This is me 0000-0002-2789-1961

Publication Date December 30, 2022
Submission Date August 18, 2022
Published in Issue Year 2022

Cite

APA Yel, G., Kayhan, M., & Ciancio, A. (2022). A new analytical approach to the (1+1)-dimensional conformable Fisher equation. Mathematical Modelling and Numerical Simulation With Applications, 2(4), 211-220. https://doi.org/10.53391/mmnsa.2022.017


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