The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method
Yıl: 2020 Cilt: 10 Sayı: 1 Sayfa Aralığı: 256 - 263 Metin Dili: İngilizce DOI: 10.37094/adyujsci.515011 İndeks Tarihi: 14-12-2021
The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method
Öz: Authors aimed to employ the sine-Gordon expansion method to acquire the new exact solutions of fractional Fitzhugh-Nagumo equation which is a stripped type of the Hodgkin-Huxley model that expresses in extensive way activation and deactivation dynamics of neuron spiking. By using the wave transformations, by the practicality of chain rule and applicability of the conformable fractional derivative, the fractional nonlinear partial differential equation (FNPDE) changes to a nonlinear ordinary differential equation. So the exact solution of the considered equation can be obtained correctly with the aid of efficient and reliable analytical techniques. Keywords: Sine-Gordon expansion method; Fitzhugh-Nagumo Equation; Conformable derivative.
Anahtar Kelime: Zaman Kesirli Fitzhugh-Nagumo Denkleminin Sine-Gordon Açılım Yöntemi İle Yeni Yürüyen Dalga Çözümleri
Öz: Yazarlar, nöron artışının, geniş bir aktivasyon ve deaktivasyon dinamiğini ifade eden Hodgkin-Huxley modelinin sade bir tipi olan kesirli Fitzhugh-Nagumo denkleminin yeni tam çözümlerini elde etmek için sine-Gordon açılım yöntemini kullanmayı amaçladılar. Dalga dönüşümleri, zincir kuralının pratikliği ve conformable kesirli türevin uygulanabilirliği kullanılarak, lineer olmayan kesirli mertebeden kısmi diferansiyel denklem, lineer olmayan adi diferansiyel denkleme dönüşür. Böylece, ele alınan denklemin tam çözümü etkin ve güvenli analitik tekniklerin yardımı ile doğru bir biçimde elde edilebilir. Anahtar Kelimeler: Sine-Gordon açılım yöntemi; Fitzhugh-Nagumo denklemi; Conformable türev.
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- Miller, K.S., Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley &Sons, New York, 1993.
- Kilbas, A., Srivastava, H.M., Trujillo, J.J., Theory and Applications of Fractional Differential Equations, Elsevier, San Diego, 2006.
- Podlubny, I., Fractional Differential Equations, Academic Press,San Diego, 1999.
- 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.
- Abdeljawad, T., On conformable fractional calculus, Journal of Computational and Applied Mathematics, 279, 57-66, 2015.
- Çenesiz, Y., Kurt, A., Taşbozan, O., On the New Solutions of the Conformable Time Fractional Generalized Hirota-Satsuma Coupled KdV System, Annals of West University of Timisoara-Mathematics and Computer Science, 55(1), 37-50, 2017.
- Taşbozan, O., Şenol, M., Kurt, A., Özkan, O., New solutions of fractional DrinfeldSokolov-Wilson system in shallow water waves, Ocean Engineering, 161, 62-68, 2018.
- Taşbozan, O., Çenesiz, Y., Kurt, A., Baleanu, D., New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method, Open Physics, 15(1), 647-651, 2017.
- Kurt, A., Taşbozan, O., Baleanu, D., New solutions for conformable fractional NizhnikNovikov-Veselov system via G′/G expansion method and homotopy analysis methods, Optical and Quantum Electronics, 49(10), 333, 2017.
- Korkmaz, A., Explicit exact solutions to some one-dimensional conformable time fractional equations, Waves in Random and Complex Media, 29(1), 124-137, 2019.
- Rosales, J.J., Godnez, F.A., Banda, V., Valencia, G.H., Analysis of the Drude model in view of the conformable derivative, Optik, 178, 1010-1015, 2019.
- Srivastava, H.M., Gunerhan, H., Analytical and approximate solutions of fractionalorder susceptible-infected-recovered epidemic model of childhood disease, Mathematical Methods in the Applied Sciences, 42(3), 935-941, 2019.
- Sabiu, J., Jibril, A., Gadu, A.M., New exact solution for the (3 +1)conformable space time fractional modified Kortewegde-Vries equations via Sine-Cosine Method, Journal of Taibah University for Science, 13(1), 91-95, 2019.
- Fitzhugh, R., Impulse and physiological states in models of nerve membrane, Biophys. J., 1, 445-466, 1961.
- Nagumo, J.S., Arimoto, S., Yoshizawa, S., An active pulse transmission line simulating nerve axon, Proc. IRE, 50, 2061-2070, 1962.
- Aronson, D.G., Weinberger, H.F., Multidimensional nonlinear diffusion arising in population genetics, Adv. Math., 30, 33-76, 1978.
- Yan, C., A simple transformation for nonlinear waves, Physics Letters A, 224(1), 77, 1996.
- Çenesiz, Y., Kurt, A., New fractional complex transform for conformable fractional partial differential equations, Journal of Applied Mathematics, Statistics and Informatics, 12, 2, 2016.
- Rubinstein, J., Sine-Gordon Equation, Journal of Mathematical Physics, 11(1), 258- 266, 1970.
| APA | Tasbozan O, Kurt A (2020). The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method. , 256 - 263. 10.37094/adyujsci.515011 |
| Chicago | Tasbozan Orkun,Kurt Ali The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method. (2020): 256 - 263. 10.37094/adyujsci.515011 |
| MLA | Tasbozan Orkun,Kurt Ali The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method. , 2020, ss.256 - 263. 10.37094/adyujsci.515011 |
| AMA | Tasbozan O,Kurt A The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method. . 2020; 256 - 263. 10.37094/adyujsci.515011 |
| Vancouver | Tasbozan O,Kurt A The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method. . 2020; 256 - 263. 10.37094/adyujsci.515011 |
| IEEE | Tasbozan O,Kurt A "The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method." , ss.256 - 263, 2020. 10.37094/adyujsci.515011 |
| ISNAD | Tasbozan, Orkun - Kurt, Ali. "The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method". (2020), 256-263. https://doi.org/10.37094/adyujsci.515011 |
| APA | Tasbozan O, Kurt A (2020). The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method. Adıyaman Üniversitesi Fen Bilimleri Dergisi, 10(1), 256 - 263. 10.37094/adyujsci.515011 |
| Chicago | Tasbozan Orkun,Kurt Ali The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method. Adıyaman Üniversitesi Fen Bilimleri Dergisi 10, no.1 (2020): 256 - 263. 10.37094/adyujsci.515011 |
| MLA | Tasbozan Orkun,Kurt Ali The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method. Adıyaman Üniversitesi Fen Bilimleri Dergisi, vol.10, no.1, 2020, ss.256 - 263. 10.37094/adyujsci.515011 |
| AMA | Tasbozan O,Kurt A The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method. Adıyaman Üniversitesi Fen Bilimleri Dergisi. 2020; 10(1): 256 - 263. 10.37094/adyujsci.515011 |
| Vancouver | Tasbozan O,Kurt A The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method. Adıyaman Üniversitesi Fen Bilimleri Dergisi. 2020; 10(1): 256 - 263. 10.37094/adyujsci.515011 |
| IEEE | Tasbozan O,Kurt A "The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method." Adıyaman Üniversitesi Fen Bilimleri Dergisi, 10, ss.256 - 263, 2020. 10.37094/adyujsci.515011 |
| ISNAD | Tasbozan, Orkun - Kurt, Ali. "The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method". Adıyaman Üniversitesi Fen Bilimleri Dergisi 10/1 (2020), 256-263. https://doi.org/10.37094/adyujsci.515011 |
