Abundant distinct types of solutions for the nervous biological fractional FitzHugh–Nagumo equation via three different sorts of schemes

Advances in Difference Equations

article

Abdel-Aty, Abdel-Haleem¹  Khater, Mostafa M. A.³  Baleanu, Dumitru⁵  Khalil, E. M.⁸  Bouslimi, Jamel⁹  Omri, M.^1,11 

[1] Department of Physics, College of Sciences, University of Bisha;Physics Department, Faculty of Science, Al-Azhar University;Department of Mathematics, Faculty of Science, Jiangsu University;Department of Mathematics, Obour Institutes;Department of Mathematics, Cankaya University;Institute of Space Sciences;Department of Medical Research, China Medical University Hospital, China Medical University;Department of Mathematics, Faculty of Science, Taif University;Department of Engineering Physics and Instrumentation, National Institute of Applied Sciences and Technology, Carthage University;Department of Physics, Faculty of Science, Taif University;Deanship of Scientific Research, King Abdulaziz University

关键词: Atangana–Baleanu (AB) fractional operator;    FitzHugh–Nagumo (FN) equation;    Analytical and numerical solutions;    Stability characteristic;   

DOI  :  10.1186/s13662-020-02852-1

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY