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Kesirli Fitzhugh-Nagumo Denkleminin Yeni Tam Çözümleri

Year 2019, Volume: 9 Issue: 3, 1633 - 1645, 01.09.2019

Orkun Tasbozan Ali Kurt

Abstract

Bu makaledeki ana amaç, reaksiyon difüzyon, sinir sinyallerinin yayılımında, devre teorisi, biyoloji ve popülasyon genetiği modeli olarak kullanılan zaman kesirli Fitzhugh-Nagumo denkleminin hareketli dalga, soliter dalga ve periyodik dalga çözümlerini elde etmektir. Bu amaç için yeni genişletilmiş direkt cebirsel yöntem kullanılmıştır. Kesirli türev ifadesi uygulanabilir, iyi tanımlı ve anlaşılabilir bir tanım olan conformable türündendir.

Keywords

Conformable Kesirli Türev Yeni Genişletilmiş Direk Cebirsel Yöntem Direk Cebirsel Yöntem Fitzhugh-Nagumo equation

References

  • Abbasbandy, S., 2008. Soliton solutions for the Fitzhugh–Nagumo equation with the homotopy analysis method. Applied Mathematical Modelling, 32(12), 2706-2714.
  • Abdeljawad T, 2015. On conformable fractional calculus. Journal of computational and Applied Mathematics, 279:57-66.
  • Aronson DG, Weinberger HF, 1978. Multidimensional nonlinear diffusion arising in population genetics. Adv. Math., 30: 33-76.
  • Atangana A, 2015. Derivative with a New Parameter, Academic Press.
  • Cenesiz Y, Tasbozan O, Kurt A, 2017. Functional Variable Method for conformable fractional modifed KdV-ZK equation and Maccari system. Tbilisi Mathematical Journal, 10: 117-125.
  • Fitzhugh R, 1961. Impulse and physiological states in models of nerve membrane. Biophys. J., 1: 445-466.
  • Hariharan, G., & Kannan, K., 2010. Haar wavelet method for solving FitzHugh-Nagumo equation. Int. J. Comput. Math. Sci, 2, 2.
  • Khalil R, Horani A, Yousef A, Sababheh M, 2014. A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264: 65-70.
  • Kumar, D., Singh, J., Baleanu, D., 2018. A new numerical algorithm for fractional Fitzhugh–Nagumo equation arising in transmission of nerve impulses. Nonlinear Dynamics, 91(1), 307-317.
  • Kurt A, Tasbozan O, Baleanu D, 2017. New solutions for conformable fractional Nizhnik– Novikov–Veselov system via G’/G expansion method and homotopy analysis methods. Optical and Quantum Electronics, 49: 333.
  • Li, H., Guo, Y., 2006. New exact solutions to the Fitzhugh–Nagumo equation. Applied Mathematics and Computation, 180(2), 524-528.
  • Nagumo JS, Arimoto S, Yoshizawa S, 1962. An active pulse transmission line simulating nerve axon,. Proc. IRE, 50:2061–2070.
  • Rezazadeh, H., 2018a. New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity. Optik, 167, 218-227.
  • Rezazadeh, H., Tariq, H., Eslami, M., Mirzazadeh, M., Zhou, Q., 2018b. New exact solutions of nonlinear conformable time-fractional Phi-4 equation. Chinese Journal of Physics, 56(6), 2805-2816.
  • Rezazadeh, H., Ali, K. K., Eslami, M., Mirzazadeh, M., Yépez-Martínez, H., 2019. On the soliton solutions to the space-time fractional simplified MCH equation. Journal of Interdisciplinary Mathematics, 1-17.
  • Taşbozan O, Kurt A, 2018b. New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 8: 295-303.
  • Taşbozan O, Senol M, Kurt A, Özkan O, 2018a. New solutions of fractional Drinfeld-Sokolov-Wilson system in shallow water waves. Ocean Engineering, 161:62-68.
  • Taşbozan O, Cenesiz Y, Kurt A, Baleanu D, 2017. New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method. Open Physics, 15:647-651.

New Exact Solutions of Fractional Fitzhugh-Nagumo Equation

Year 2019, Volume: 9 Issue: 3, 1633 - 1645, 01.09.2019

Orkun Tasbozan Ali Kurt

Abstract

The main aim of this article is obtaining the travelling wave, solitary wave and periodic wave solutions for time fractional Fitzhugh-Nagumo equation which used as a model for reaction–diffusion, transmission of nerve impulses, circuit theory, biology and population genetics. The new extended direct algebraic method is employed for this aim. The fractional derivative is in conformable sense which is an applicable, well behaved and understandable definition.

Keywords

Fitzhugh-Nagumo equation fractional derivative New extended direct algebraic method Fitzhugh-Nagumo equation

References

  • Abbasbandy, S., 2008. Soliton solutions for the Fitzhugh–Nagumo equation with the homotopy analysis method. Applied Mathematical Modelling, 32(12), 2706-2714.
  • Abdeljawad T, 2015. On conformable fractional calculus. Journal of computational and Applied Mathematics, 279:57-66.
  • Aronson DG, Weinberger HF, 1978. Multidimensional nonlinear diffusion arising in population genetics. Adv. Math., 30: 33-76.
  • Atangana A, 2015. Derivative with a New Parameter, Academic Press.
  • Cenesiz Y, Tasbozan O, Kurt A, 2017. Functional Variable Method for conformable fractional modifed KdV-ZK equation and Maccari system. Tbilisi Mathematical Journal, 10: 117-125.
  • Fitzhugh R, 1961. Impulse and physiological states in models of nerve membrane. Biophys. J., 1: 445-466.
  • Hariharan, G., & Kannan, K., 2010. Haar wavelet method for solving FitzHugh-Nagumo equation. Int. J. Comput. Math. Sci, 2, 2.
  • Khalil R, Horani A, Yousef A, Sababheh M, 2014. A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264: 65-70.
  • Kumar, D., Singh, J., Baleanu, D., 2018. A new numerical algorithm for fractional Fitzhugh–Nagumo equation arising in transmission of nerve impulses. Nonlinear Dynamics, 91(1), 307-317.
  • Kurt A, Tasbozan O, Baleanu D, 2017. New solutions for conformable fractional Nizhnik– Novikov–Veselov system via G’/G expansion method and homotopy analysis methods. Optical and Quantum Electronics, 49: 333.
  • Li, H., Guo, Y., 2006. New exact solutions to the Fitzhugh–Nagumo equation. Applied Mathematics and Computation, 180(2), 524-528.
  • Nagumo JS, Arimoto S, Yoshizawa S, 1962. An active pulse transmission line simulating nerve axon,. Proc. IRE, 50:2061–2070.
  • Rezazadeh, H., 2018a. New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity. Optik, 167, 218-227.
  • Rezazadeh, H., Tariq, H., Eslami, M., Mirzazadeh, M., Zhou, Q., 2018b. New exact solutions of nonlinear conformable time-fractional Phi-4 equation. Chinese Journal of Physics, 56(6), 2805-2816.
  • Rezazadeh, H., Ali, K. K., Eslami, M., Mirzazadeh, M., Yépez-Martínez, H., 2019. On the soliton solutions to the space-time fractional simplified MCH equation. Journal of Interdisciplinary Mathematics, 1-17.
  • Taşbozan O, Kurt A, 2018b. New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 8: 295-303.
  • Taşbozan O, Senol M, Kurt A, Özkan O, 2018a. New solutions of fractional Drinfeld-Sokolov-Wilson system in shallow water waves. Ocean Engineering, 161:62-68.
  • Taşbozan O, Cenesiz Y, Kurt A, Baleanu D, 2017. New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method. Open Physics, 15:647-651.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Orkun Tasbozan 0000-0001-5003-6341

Ali Kurt 0000-0002-0617-6037

Publication Date September 1, 2019
Submission Date January 15, 2019
Acceptance Date June 14, 2019
Published in Issue Year 2019 Volume: 9 Issue: 3

Cite

APA Tasbozan, O., & Kurt, A. (2019). New Exact Solutions of Fractional Fitzhugh-Nagumo Equation. Journal of the Institute of Science and Technology, 9(3), 1633-1645.
AMA Tasbozan O, Kurt A. New Exact Solutions of Fractional Fitzhugh-Nagumo Equation. J. Inst. Sci. and Tech. September 2019;9(3):1633-1645.
Chicago Tasbozan, Orkun, and Ali Kurt. “New Exact Solutions of Fractional Fitzhugh-Nagumo Equation”. Journal of the Institute of Science and Technology 9, no. 3 (September 2019): 1633-45.
EndNote Tasbozan O, Kurt A (September 1, 2019) New Exact Solutions of Fractional Fitzhugh-Nagumo Equation. Journal of the Institute of Science and Technology 9 3 1633–1645.
IEEE O. Tasbozan and A. Kurt, “New Exact Solutions of Fractional Fitzhugh-Nagumo Equation”, J. Inst. Sci. and Tech., vol. 9, no. 3, pp. 1633–1645, 2019.
ISNAD Tasbozan, Orkun - Kurt, Ali. “New Exact Solutions of Fractional Fitzhugh-Nagumo Equation”. Journal of the Institute of Science and Technology 9/3 (September 2019), 1633-1645.
JAMA Tasbozan O, Kurt A. New Exact Solutions of Fractional Fitzhugh-Nagumo Equation. J. Inst. Sci. and Tech. 2019;9:1633–1645.
MLA Tasbozan, Orkun and Ali Kurt. “New Exact Solutions of Fractional Fitzhugh-Nagumo Equation”. Journal of the Institute of Science and Technology, vol. 9, no. 3, 2019, pp. 1633-45.
Vancouver Tasbozan O, Kurt A. New Exact Solutions of Fractional Fitzhugh-Nagumo Equation. J. Inst. Sci. and Tech. 2019;9(3):1633-45.