Abundant distinct types of solutions for the nervous biological fractional FitzHugh–Nagumo equation via three different sorts of schemes
Abstract The dynamical attitude of the transmission for the nerve impulses of a nervous system, which is mathematically formulated by the Atangana–Baleanu (AB) time-fractional FitzHugh–Nagumo (FN) equation, is computationally and numerically investigated via two distinct schemes. These schemes are t...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-09-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02852-1 |
| _version_ | 1818205570522415104 |
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| author | Abdel-Haleem Abdel-Aty Mostafa M. A. Khater Dumitru Baleanu E. M. Khalil Jamel Bouslimi M. Omri |
| author_facet | Abdel-Haleem Abdel-Aty Mostafa M. A. Khater Dumitru Baleanu E. M. Khalil Jamel Bouslimi M. Omri |
| author_sort | Abdel-Haleem Abdel-Aty |
| collection | DOAJ |
| description | Abstract The dynamical attitude of the transmission for the nerve impulses of a nervous system, which is mathematically formulated by the Atangana–Baleanu (AB) time-fractional FitzHugh–Nagumo (FN) equation, is computationally and numerically investigated via two distinct schemes. These schemes are the improved Riccati expansion method and B-spline schemes. Additionally, the stability behavior of the analytical evaluated solutions is illustrated based on the characteristics of the Hamiltonian to explain the applicability of them in the model’s applications. Also, the physical and dynamical behaviors of the gained solutions are clarified by sketching them in three different types of plots. The practical side and power of applied methods are shown to explain their ability to use on many other nonlinear evaluation equations. |
| first_indexed | 2024-12-12T03:59:14Z |
| format | Article |
| id | doaj.art-eb8707c854e745ffb9a6454269e1bc0e |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-12T03:59:14Z |
| publishDate | 2020-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-eb8707c854e745ffb9a6454269e1bc0e2022-12-22T00:39:08ZengSpringerOpenAdvances in Difference Equations1687-18472020-09-012020111710.1186/s13662-020-02852-1Abundant distinct types of solutions for the nervous biological fractional FitzHugh–Nagumo equation via three different sorts of schemesAbdel-Haleem Abdel-Aty0Mostafa M. A. Khater1Dumitru Baleanu2E. M. Khalil3Jamel Bouslimi4M. Omri5Department of Physics, College of Sciences, University of BishaDepartment of Mathematics, Faculty of Science, Jiangsu UniversityDepartment of Mathematics, Cankaya UniversityDepartment of Mathematics, Faculty of Science, Taif UniversityDepartment of Engineering Physics and Instrumentation, National Institute of Applied Sciences and Technology, Carthage UniversityDeanship of Scientific Research, King Abdulaziz UniversityAbstract The dynamical attitude of the transmission for the nerve impulses of a nervous system, which is mathematically formulated by the Atangana–Baleanu (AB) time-fractional FitzHugh–Nagumo (FN) equation, is computationally and numerically investigated via two distinct schemes. These schemes are the improved Riccati expansion method and B-spline schemes. Additionally, the stability behavior of the analytical evaluated solutions is illustrated based on the characteristics of the Hamiltonian to explain the applicability of them in the model’s applications. Also, the physical and dynamical behaviors of the gained solutions are clarified by sketching them in three different types of plots. The practical side and power of applied methods are shown to explain their ability to use on many other nonlinear evaluation equations.http://link.springer.com/article/10.1186/s13662-020-02852-1Atangana–Baleanu (AB) fractional operatorFitzHugh–Nagumo (FN) equationAnalytical and numerical solutionsStability characteristic |
| spellingShingle | Abdel-Haleem Abdel-Aty Mostafa M. A. Khater Dumitru Baleanu E. M. Khalil Jamel Bouslimi M. Omri Abundant distinct types of solutions for the nervous biological fractional FitzHugh–Nagumo equation via three different sorts of schemes Advances in Difference Equations Atangana–Baleanu (AB) fractional operator FitzHugh–Nagumo (FN) equation Analytical and numerical solutions Stability characteristic |
| title | Abundant distinct types of solutions for the nervous biological fractional FitzHugh–Nagumo equation via three different sorts of schemes |
| title_full | Abundant distinct types of solutions for the nervous biological fractional FitzHugh–Nagumo equation via three different sorts of schemes |
| title_fullStr | Abundant distinct types of solutions for the nervous biological fractional FitzHugh–Nagumo equation via three different sorts of schemes |
| title_full_unstemmed | Abundant distinct types of solutions for the nervous biological fractional FitzHugh–Nagumo equation via three different sorts of schemes |
| title_short | Abundant distinct types of solutions for the nervous biological fractional FitzHugh–Nagumo equation via three different sorts of schemes |
| title_sort | abundant distinct types of solutions for the nervous biological fractional fitzhugh nagumo equation via three different sorts of schemes |
| topic | Atangana–Baleanu (AB) fractional operator FitzHugh–Nagumo (FN) equation Analytical and numerical solutions Stability characteristic |
| url | http://link.springer.com/article/10.1186/s13662-020-02852-1 |
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